Editing Binary number (section)

===Multiplication===<!-- This section is linked from [[Binary-coded decimal]] -->
[[Multiplication]] in binary is similar to its decimal counterpart. Two numbers {{varserif|A}} and {{varserif|B}} can be multiplied by partial products: for each digit in {{varserif|B}}, the product of that digit in {{varserif|A}} is calculated and written on a new line, shifted leftward so that its rightmost digit lines up with the digit in {{varserif|B}} that was used. The sum of all these partial products gives the final result.

Since there are only two digits in binary, there are only two possible outcomes of each partial multiplication:
* If the digit in {{varserif|B}} is 0, the partial product is also 0
* If the digit in {{varserif|B}} is 1, the partial product is equal to {{varserif|A}}

For example, the binary numbers 1011 and 1010 are multiplied as follows:

            1 0 1 1   ({{varserif|A}})
          × 1 0 1 0   ({{varserif|B}})
          ---------
            0 0 0 0   ← to the rightmost 'zero' in {{varserif|B}}
    +     1 0 1 1     ← to the next 'one' in {{varserif|B}}
    +   0 0 0 0
    + 1 0 1 1
    ---------------
    = 1 1 0 1 1 1 0

Binary numbers can also be multiplied with bits after a [[binary point]]:

                1 0 1 . 1 0 1     {{varserif|A}} (5.625 in decimal)
              × 1 1 0 . 0 1       {{varserif|B}} (6.25 in decimal)
              -------------------
                    1 . 0 1 1 0 1   ← to a 'one' in {{varserif|B}}
      +           0 0 . 0 0 0 0     ← to a 'zero' in {{varserif|B}}
      +         0 0 0 . 0 0 0
      +       1 0 1 1 . 0 1
      +     1 0 1 1 0 . 1
      ---------------------------
      =   1 0 0 0 1 1 . 0 0 1 0 1 (35.15625 in decimal)

See also [[Booth's multiplication algorithm]].

====Multiplication table====
{| class="wikitable" style="text-align:center"
|-
! style="width:1.5em" |
! style="width:1.5em" | 0
! style="width:1.5em" | 1
|-
! 0
| 0
| 0
|-
! 1
| 0
| 1
|}

The binary multiplication table is the same as the [[Logical conjunction#Truth table|truth table]] of the [[logical conjunction]] operation <math>\land</math>.