Editing Binary-coded decimal (section)

=={{anchor|Unpacked BCD|NBCD|8421|8-4-2-1}}Background==
BCD takes advantage of the fact that any one decimal numeral can be represented by a four-bit pattern. An obvious way of encoding digits is ''Natural BCD'' (NBCD), where each decimal digit is represented by its corresponding four-bit binary value, as shown in the following table. This is also called "8421" encoding.

{| class="wikitable" style="text-align:center;"
|-
! scope="col" rowspan="2" | Decimal digit
! scope="col" colspan="4" | BCD
|-
! 8 !! 4 !! 2 !! 1
|-
| 0 || 0 || 0 || 0 || 0
|-
| 1 || 0 || 0 || 0 || 1
|-
| 2 || 0 || 0 || 1 || 0
|-
| 3 || 0 || 0 || 1 || 1
|-
| 4 || 0 || 1 || 0 || 0
|-
| 5 || 0 || 1 || 0 || 1
|-
| 6 || 0 || 1 || 1 || 0
|-
| 7 || 0 || 1 || 1 || 1
|-
| 8 || 1 || 0 || 0 || 0
|-
| 9 || 1 || 0 || 0 || 1
|}

This scheme can also be referred to as ''Simple Binary-Coded Decimal'' (''SBCD'') or ''BCD&nbsp;8421'', and is the most common encoding.<ref name="Evans_1961"/> Others include the so-called "4221" and "7421" encoding – named after the weighting used for the bits – and "[[Excess-3]]".<ref name="Lala_2007"/> For example, the BCD digit 6, {{code|0110'b}} in 8421 notation, is {{code|1100'b}} in 4221 (two encodings are possible), {{code|0110'b}} in 7421, while in Excess-3 it is {{code|1001'b}} (<math>6 + 3 = 9</math>).

{| class="wikitable" style="text-align:center;"
|+ 4-bit BCD codes and pseudo-tetrades
! Bit !! Weight !! style="background:lightgray"|&nbsp;0 !! style="background:lightgray"|&nbsp;1 !! style="background:lightgray"|&nbsp;2 !! style="background:lightgray"|&nbsp;3 !! style="background:lightgray"|&nbsp;4 !! style="background:lightgray"|&nbsp;5 !! style="background:lightgray"|&nbsp;6 !! style="background:lightgray"|&nbsp;7 !! style="background:lightgray"|&nbsp;8 !! style="background:lightgray"|&nbsp;9 !! style="background:lightgray"|10 !! style="background:lightgray"|11 !! style="background:lightgray"|12 !! style="background:lightgray"|13 !! style="background:lightgray"|14 !! style="background:lightgray"|15 !! &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Comment&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
|-
| 4 || style="background:lightgray"|8 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || rowspan="4"|'''Binary'''
|-
| 3 || style="background:lightgray"|4 || 0 || 0 || 0 || 0 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || 0 || 0 || 0 || 0 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1 || style="background:#0FF"|1
|-
| 2 || style="background:lightgray"|2 || 0 || 0 || style="background:#0FF"|1 || style="background:#0FF"|1 || 0 || 0 || style="background:#0FF"|1 || style="background:#0FF"|1 || 0 || 0 || style="background:#0FF"|1 || style="background:#0FF"|1 || 0 || 0 || style="background:#0FF"|1 || style="background:#0FF"|1
|-
| 1 || style="background:lightgray"|1 || 0 || style="background:#0FF"|1 || 0 || style="background:#0FF"|1 || 0 || style="background:#0FF"|1 || 0 || style="background:#0FF"|1 || 0 || style="background:#0FF"|1 || 0 || style="background:#0FF"|1 || 0 || style="background:#0FF"|1 || 0 || style="background:#0FF"|1
|-
| colspan="19"|
|-
| colspan="2"|'''Name''' || style="background:lightgray"|0 || style="background:lightgray"|1 || style="background:lightgray"|2 || style="background:lightgray"|3 || style="background:lightgray"|4 || style="background:lightgray"|5 || style="background:lightgray"|6 || style="background:lightgray"|7 || style="background:lightgray"|8 || style="background:lightgray"|9 || style="background:lightgray"|10 || style="background:lightgray"|11 || style="background:lightgray"|12 || style="background:lightgray"|13 || style="background:lightgray"|14 || style="background:lightgray"|15 || '''Decimal'''
|-
| colspan="19"|
|-
| colspan="2"|'''8&thinsp;4&thinsp;2&thinsp;1 (XS-0)''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || style="background:gray"|10 || style="background:gray"|11 || style="background:gray"|12 || style="background:gray"|13 || style="background:gray"|14 || style="background:gray"|15 || <!-- <ref name="Kautz_1954"/> --><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Kämmerer_1969"/><ref name="Dokter_1973"/><ref name="Dokter_1975"/><ref group="nb" name="Non-BCD"/>
|-
| colspan="19"|
|-
| {{anchor|7421}}colspan="2"|'''7&thinsp;4&thinsp;2&thinsp;1''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:gray"|&nbsp; || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || <ref name="Kautz_1954"/><ref name="Chinal_1973"/><ref name="MIL_1991"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[Aiken code|Aiken]] (2&thinsp;4&thinsp;2&thinsp;1)}}''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || <!-- <ref name="Kautz_1954"/> --><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Kämmerer_1969"/><ref name="Dokter_1973"/><ref name="Dokter_1975"/><ref group="nb" name="Aiken_2421"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[Excess-3 code|Excess-3]] (XS-3)}}''' || style="background:gray"|-3 || style="background:gray"|-2 || style="background:gray"|-1 || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || style="background:gray"|10 || style="background:gray"|11 || style="background:gray"|12 || <!-- <ref name="Kautz_1954"/> --><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Kämmerer_1969"/><ref name="Dokter_1973"/><ref name="Dokter_1975"/><ref group="nb" name="Non-BCD"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[Excess-6 code|Excess-6]] (XS-6)}}''' || style="background:gray"|-6 || style="background:gray"|-5 || style="background:gray"|-4 || style="background:gray"|-3 || style="background:gray"|-2 || style="background:gray"|-1 || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || <ref name="Kautz_1954"/><ref group="nb" name="Non-BCD"/>
|-
| colspan="19"|
|-
| {{anchor|Jump-at-2}}colspan="2"|'''Jump-at-2 (<!-- special -->2&thinsp;4&thinsp;2&thinsp;1)''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || <ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| {{anchor|Jump-at-2}}colspan="2"|{{nowrap|'''Jump-at-8 (<!-- unsymmetrical -->2&thinsp;4&thinsp;2&thinsp;1)'''}} || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|9 || <ref name="Stopper_1960"/><ref name="Borucki-Dittmann_1971"/><ref name="Dokter_1973"/><ref name="Dokter_1975"/><ref group="nb" name="Unsymmetrical_2421"/>
|-
| colspan="19"|
|-
| {{anchor|4221}}colspan="2"|{{nowrap|'''4&thinsp;2&thinsp;2&thinsp;1 (I)'''}} || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || <ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| {{anchor|4221 II}}colspan="2"|{{nowrap|'''4&thinsp;2&thinsp;2&thinsp;1 (II)'''}} || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|9 || <ref name="Stopper_1960"/><ref name="Borucki-Dittmann_1971"/>
|-
| colspan="19"|
|-
| {{anchor|5421}}colspan="2"|'''5&thinsp;4&thinsp;2&thinsp;1''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || <ref name="Kautz_1954"/><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| {{anchor|5221}}colspan="2"|'''5&thinsp;2&thinsp;2&thinsp;1''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:gray"|&nbsp; || <ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| {{anchor|5121}}colspan="2"|'''5&thinsp;1&thinsp;2&thinsp;1''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|9 || <ref name="Chinal_1973"/>
|-
| colspan="19"|
|-
| {{anchor|5311}}colspan="2"|'''5&thinsp;3&thinsp;1&thinsp;1''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:gray"|&nbsp; || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || <ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| {{anchor|White}}colspan="2"|'''{{nowrap|White (5&thinsp;2&thinsp;1&thinsp;1)}}''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:gray"|&nbsp; || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:gray"|&nbsp; || style="background:#0FF"|9 || <ref name="White_1953"/><ref name="Kautz_1954"/><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| {{anchor|5211}}colspan="2"|'''5&thinsp;2&thinsp;1&thinsp;1''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || style="background:#0FF"|6 || style="background:gray"|&nbsp; || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|9 || <ref name="EHub_2015"/>
|-
| colspan="19"|
|-
| colspan="2"|&nbsp; || style="background:lightgray"|0 || style="background:lightgray"|1 || style="background:lightgray"|2 || style="background:lightgray"|3 || style="background:lightgray"|4 || style="background:lightgray"|5 || style="background:lightgray"|6 || style="background:lightgray"|7 || style="background:lightgray"|8 || style="background:lightgray"|9 || style="background:lightgray"|10 || style="background:lightgray"|11 || style="background:lightgray"|12 || style="background:lightgray"|13 || style="background:lightgray"|14 || style="background:lightgray"|15 ||
|-
| colspan="19"|
|-
| {{anchor|Tape}}colspan="2"|'''Magnetic&nbsp;tape''' || style="background:gray"|&nbsp; || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|9 || style="background:#0FF"|0 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || <ref name="Kämmerer_1969"/>
|-
| colspan="19"|
|-
| {{anchor|Paul}}colspan="2"|'''Paul''' || style="background:gray"|&nbsp; || style="background:#0FF"|1 || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|5 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:#0FF"|0 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || <ref name="Paul_1995"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[Gray BCD code|Gray]]}}''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:#0FF"|6 || style="background:#0FF" |7 || style="background:#0FF" |5 || style="background:#0FF" |4 || style="background:gray" |15 || style="background:gray"|14 || style="background:gray"|12 || style="background:gray"|13 || style="background:#0FF"|8 || style="background:#0FF"|9 || style="background:gray"|11 || style="background:gray"|10 || <ref name="Gray_1947"/><!-- <ref name="Kautz_1954"/> --><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Kämmerer_1969"/><ref name="Dokter_1973"/><ref name="Dokter_1975"/><ref group="nb" name="Non-BCD"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[Glixon code|Glixon]]}}''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:#0FF"|5 || style="background:#0FF"|4 || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || <ref name="Glixon_1957"/><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Kämmerer_1969"/><ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| {{anchor|Ledley}}colspan="2"|'''Ledley''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF|3 || style="background:#0FF"|2 || style="background:#0FF"|7 || style="background:#0FF"|6 || style="background:#0FF"|4 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:gray"|&nbsp; || <ref name="Ledley_1960"/>
|-
| colspan="19"|
|-
| {{anchor|4311}}colspan="2"|'''4&thinsp;3&thinsp;1&thinsp;1''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|9 || <ref name="Chinal_1973"/>
|-
| colspan="19"|
|-
| {{anchor|LARC}}colspan="2"|'''[[UNIVAC LARC|LARC]]''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:#0FF"|3 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:gray"|&nbsp; || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:#0FF"|8 || <ref name="Savard_2018_Decimal"/>
|-
| colspan="19"|
|-
| {{anchor|Klar}}colspan="2"|'''Klar''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:#0FF"|3 || style="background:#0FF"|9 || style="background:#0FF"|8 || style="background:gray"|&nbsp; || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:#0FF"|6 || <ref name="Klar_1970"/><ref name="Klar_1989"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[Petherick code|Petherick]] (RAE)}}''' || style="background:gray"|&nbsp; || style="background:#0FF"|1 || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:#0FF"|0 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || <ref name="Petherick_1953"/><ref name="Petherick-Hopkins_1958"/><ref group="nb" name="Petherick_RAE"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[O'Brien code I|O'Brien I]] (Watts)}}''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:#0FF"|8 || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:gray"|&nbsp; || <ref name="O'Brien_1955"/><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Dokter_1973"/><ref name="Dokter_1975"/><ref group="nb" name="O'Brien-I_WRD"/>
|-
| colspan="19"|
|-
| {{anchor|5-cyclic}}colspan="2"|'''5-cyclic''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF|3 || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|8 || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:gray"|&nbsp; || <ref name="Ledley_1960"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[Tompkins code I|Tompkins I]]}}''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|7 || style="background:#0FF"|5 || style="background:#0FF"|6 || <ref name="Tompkins_1956"/><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| {{anchor|Lippel}}colspan="2"|'''Lippel''' || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|7 || style="background:#0FF"|6 || style="background:#0FF"|5 || <ref name="Lippel_1955"/><ref name="Susskind_1958"/><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> -->
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[O'Brien code II|O'Brien II]]}}''' || style="background:gray"|&nbsp; || style="background:#0FF"|0 || style="background:#0FF"|2 || style="background:#0FF"|1 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:#0FF"|7 || style="background:#0FF"|8 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || style="background:#0FF"|6 || style="background:gray"|&nbsp; || <ref name="O'Brien_1955"/><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[Tompkins code II|Tompkins II]]}}''' || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|0 || style="background:#0FF"|1 || style="background:#0FF"|4 || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:#0FF"|7 || style="background:#0FF"|9 || style="background:#0FF"|8 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || <ref name="Tompkins_1956"/><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> --><ref name="Dokter_1973"/><ref name="Dokter_1975"/>
|-
| colspan="19"|
|-
| colspan="2"|'''{{nowrap|[[Excess-3 Gray code|Excess-3 Gray]]}}''' || style="background:gray"|-3 || style="background:gray"|-2 || style="background:#0FF"|0 || style="background:gray"|-1 || style="background:#0FF"|4 || style="background:#0FF"|3 || style="background:#0FF"|1 || style="background:#0FF"|2 || style="background:gray"|12 || style="background:gray"|11 || style="background:#0FF"|9 || style="background:gray"|10 || style="background:#0FF"|5 || style="background:#0FF"|6 || style="background:#0FF"|8 || style="background:#0FF"|7 || <ref name="Dokter_1973"/><ref name="Dokter_1975"/><ref name="MIL_1991"/><ref group="nb" name="Gray_Stibitz"/><ref group="nb" name="Non-BCD"/>
|-
| colspan="19"|
|-
| {{anchor|63−2−1}}colspan="2"|'''6&thinsp;3&thinsp;−2&thinsp;−1 (I)''' || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:#0FF"|1 || style="background:#0FF"|0 || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:#0FF"|4 || style="background:#0FF"|8 || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:#0FF"|7 || style="background:#0FF"|6 || <ref name="Savard_2018_Decimal"/><ref name="Yuen_1977"/>
|-
| colspan="19"|
|-
| {{anchor|63−2−1 II}}colspan="2"|'''6&thinsp;3&thinsp;−2&thinsp;−1 (II)''' || style="background:#0FF"|0 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|6 || style="background:#0FF"|5 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:#0FF"|8 || style="background:#0FF"|7 || style="background:gray"|&nbsp; || <ref name="Savard_2018_Decimal"/><ref name="Yuen_1977"/>
|-
| colspan="19"|
|-
| {{anchor|84−2−1}}colspan="2"|'''8&thinsp;4&thinsp;−2&thinsp;−1''' || style="background:#0FF"|0 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:#0FF"|1 || style="background:#0FF"|8 || style="background:#0FF"|7 || style="background:#0FF"|6 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|9 || <ref name="Savard_2018_Decimal"/>
|-
| colspan="19"|
|-
| {{anchor|Lucal}}colspan="2"|'''[[Lucal code|Lucal]]''' || style="background:#0FF"|0 || style="background:gray"|15 || style="background:gray"|14 || style="background:#0FF"|1 || style="background:gray"|12 || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:gray"|13 || style="background:#0FF"|8 || style="background:#0FF"|7 || style="background:#0FF"|6 || style="background:#0FF"|9 || style="background:#0FF"|4 || style="background:gray"|11 || style="background:gray"|10 || style="background:#0FF"|5 || <ref name="Lucal_1959"/>
|-
| colspan="19"|
|-
| {{anchor|Kautz}}colspan="2"|'''Kautz I''' || style="background:#0FF"|0 || style="background:gray"|&nbsp; || style="background:gray"|&nbsp; || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:#0FF"|5 || style="background:#0FF"|1 || style="background:#0FF"|3 || style="background:gray"|&nbsp; || style="background:#0FF"|7 || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|6 || style="background:gray"|&nbsp; || style="background:#0FF"|4 || <ref name="Kautz_1954"/>
|-
| colspan="19"|
|-
| {{anchor|Kautz II}}colspan="2"|'''Kautz II''' || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:#0FF"|8 || style="background:gray"|&nbsp; || style="background:#0FF"|6 || style="background:#0FF"|7 || style="background:gray"|&nbsp; || style="background:#0FF"|0 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || <ref name="Kautz_1954"/><ref name="Steinbuch_1962"/><!-- <ref name="Steinbuch-Wagner_1967"/><ref name="Steinbuch-Weber-Heinemann_1974"/> -->
|-
| colspan="19"|
|-
| {{anchor|Susskind}}colspan="2"|'''Susskind I''' || style="background:gray"|&nbsp; || style="background:#0FF"|0 || style="background:gray"|&nbsp; || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|4 || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || style="background:#0FF"|6 || style="background:#0FF"|7 || <ref name="Susskind_1958"/>
|-
| colspan="19"|
|-
| {{anchor|Susskind II}}colspan="2"|'''Susskind II''' || style="background:gray"|&nbsp; || style="background:#0FF"|0 || style="background:gray"|&nbsp; || style="background:#0FF"|1 || style="background:gray"|&nbsp; || style="background:#0FF"|9 || style="background:gray"|&nbsp; || style="background:#0FF"|8 || style="background:#0FF"|4 || style="background:gray"|&nbsp; || style="background:#0FF"|3 || style="background:#0FF"|2 || style="background:#0FF"|5 || style="background:gray"|&nbsp; || style="background:#0FF"|6 || style="background:#0FF"|7 || <ref name="Susskind_1958"/>
|-
| colspan="19"|
|-
| colspan="2"|&nbsp; || style="background:lightgray"|0 || style="background:lightgray"|1 || style="background:lightgray"|2 || style="background:lightgray"|3 || style="background:lightgray"|4 || style="background:lightgray"|5 || style="background:lightgray"|6 || style="background:lightgray"|7 || style="background:lightgray"|8 || style="background:lightgray"|9 || style="background:lightgray"|10 || style="background:lightgray"|11 || style="background:lightgray"|12 || style="background:lightgray"|13 || style="background:lightgray"|14 || style="background:lightgray"|15 ||
|}

The following table represents [[decimal]] digits from 0 to 9 in various BCD encoding systems. In the headers, the "<code>8{{thinsp}}4{{thinsp}}2{{thinsp}}1</code>" indicates the weight of each bit. In the fifth column ("BCD&nbsp;8{{thinsp}}4{{thinsp}}−2{{thinsp}}−1"), two of the weights are negative. Both ASCII and EBCDIC character codes for the digits, which are examples of zoned BCD, are also shown.

{| class="wikitable" style="margin:auto;"
|-
! style="background:#e0e0e0;"| &nbsp;<br />Digit
! style="background:#e0e0e0;"| BCD<br />8{{thinsp}}4{{thinsp}}2{{thinsp}}1
! style="background:#e0e0e0;"| [[George Stibitz|Stibitz]]&nbsp;code or [[Excess-3]]
! style="background:#e0e0e0;"| [[Aiken-Code]] or BCD<br />2{{thinsp}}4{{thinsp}}2{{thinsp}}1
! style="background:#e0e0e0;"| BCD<br />8{{thinsp}}4{{thinsp}}−2{{thinsp}}−1
! style="background:#e0e0e0;"| {{nowrap| [[IBM 702]], }} {{nowrap| [[IBM 705]], }} {{nowrap| [[IBM 7080]], }} {{nowrap| [[IBM 1401]] }}<br /> 8{{thinsp}}4{{thinsp}}2{{thinsp}}1
! style="background:#e0e0e0;"| [[ASCII]] <br />0000&nbsp;8421
! style="background:#e0e0e0;"| [[EBCDIC]] <br />0000&nbsp;8421
|- style="text-align:center;"
! style="background:#f0f0f0;"|0
| 0000
| 0011
| 0000
| 0000
| 1010
| 0011&nbsp;0000
| 1111&nbsp;0000
|- style="text-align:center;"
! style="background:#f0f0f0;"|1
| 0001
| 0100
| 0001
| 0111
| 0001
| 0011&nbsp;0001
| 1111&nbsp;0001
|- style="text-align:center;"
! style="background:#f0f0f0;"|2
| 0010
| 0101
| 0010
| 0110
| 0010
| 0011&nbsp;0010
| 1111&nbsp;0010
|- style="text-align:center;"
! style="background:#f0f0f0;"|3
| 0011
| 0110
| 0011
| 0101
| 0011
| 0011&nbsp;0011
| 1111&nbsp;0011
|- style="text-align:center;"
! style="background:#f0f0f0;"|4
| 0100
| 0111
| 0100
| 0100
| 0100
| 0011&nbsp;0100
| 1111&nbsp;0100
|- style="text-align:center;"
! style="background:#f0f0f0;"|5
| 0101
| 1000
| 1011
| 1011
| 0101
| 0011&nbsp;0101
| 1111&nbsp;0101
|- style="text-align:center;"
! style="background:#f0f0f0;"|6
| 0110
| 1001
| 1100
| 1010
| 0110
| 0011 0110
| 1111 0110
|- style="text-align:center;"
! style="background:#f0f0f0;"|7
| 0111
| 1010
| 1101
| 1001
| 0111
| 0011&nbsp;0111
| 1111&nbsp;0111
|- style="text-align:center;"
! style="background:#f0f0f0;"|8
| 1000
| 1011
| 1110
| 1000
| 1000
| 0011&nbsp;1000
| 1111&nbsp;1000
|- style="text-align:center;"
! style="background:#f0f0f0;"|9
| 1001
| 1100
| 1111
| 1111
| 1001
| 0011&nbsp;1001
| 1111&nbsp;1001
|}

As most computers deal with data in 8-bit [[byte]]s, it is possible to use one of the following methods to encode a BCD number:
* '''Unpacked''': Each decimal digit is encoded into one byte, with four bits representing the number and the remaining bits having no significance.
* '''Packed''': Two decimal digits are encoded into a single byte, with one digit in the least significant [[nibble]] ([[Bit numbering#Most- vs least-significant bit first|bits 0 through 3]]) and the other numeral in the most significant nibble (bits 4 through 7).<ref group="nb" name="Packed_chars"/>

As an example, encoding the decimal number <code>'''91'''</code> using unpacked BCD results in the following binary pattern of two bytes:
 Decimal:         9         1
 Binary : 0000 1001 0000 0001

In packed BCD, the same number would fit into a single byte:
 Decimal:    9    1
 Binary : 1001 0001

Hence the numerical range for one unpacked BCD byte is zero through nine inclusive, whereas the range for one packed BCD byte is zero through ninety-nine inclusive.

To represent numbers larger than the range of a single byte any number of contiguous bytes may be used. For example, to represent the decimal number <code>'''12345'''</code> in packed BCD, using [[big-endian]] format, a program would encode as follows:
 Decimal:    0    1    2    3    4    5
 Binary : 0000 0001 0010 0011 0100 0101

Here, the most significant nibble of the most significant byte has been encoded as zero, so the number is stored as <code>'''012345'''</code> (but formatting routines might replace or remove leading zeros). Packed BCD is more efficient in storage usage than unpacked BCD; encoding the same number (with the leading zero) in unpacked format would consume twice the storage.

[[Logical shift|Shifting]] and [[mask (computing)|masking]] operations are used to pack or unpack a packed BCD digit. Other [[bitwise operation]]s are used to convert a numeral to its equivalent bit pattern or reverse the process.