Editing Quine–McCluskey algorithm (section)

===Step 2: Prime implicant chart===
None of the terms can be combined any further than this, so at this point we construct an essential prime implicant table. Along the side goes the prime implicants that have just been generated (these are the ones that have been marked with a "{{color|red|*}}" in the previous step), and along the top go the minterms specified earlier. The don't care terms are not placed on top—they are omitted from this section because they are not necessary inputs.

:{| class="wikitable" style="text-align:center;"
|-
!                             || 4 || 8 || 10 || 11 || 12 || 15 || ⇒ || A || B || C || D
|-
| style="text-align:left;" | m(4,12) {{color|blue|<sup>#</sup>}}        || {{Ya|✓}} || || || || {{Ya|✓}} ||   || ⇒ || {{sdash}} || 1 || 0 || 0
|-
| style="text-align:left;" | m(8,9,10,11)    || || {{Ya|✓}} || {{Ya|✓}} || {{Ya|✓}} || || || ⇒ || 1 || 0 || {{sdash}} || {{sdash}}
|-
| style="text-align:left;" | m(8,10,12,14)   || || {{Ya|✓}} || {{Ya|✓}} || || {{Ya|✓}} || || ⇒ || 1 || {{sdash}} || {{sdash}} || 0
|-
| style="text-align:left;" | m(10,11,14,15) {{color|blue|<sup>#</sup>}} || || || {{Ya|✓}} || {{Ya|✓}} || || {{Ya|✓}} || ⇒ || 1 || {{sdash}} || 1 || {{sdash}}
|}

To find the essential prime implicants, we look for columns with only one "✓". If a column has only one "✓", this means that the minterm can only be covered by one prime implicant. This prime implicant is ''essential''.

For example: in the first column, with minterm 4, there is only one "✓". This means that m(4,12) is essential (hence marked by {{color|blue|<sup>#</sup>}}). Minterm 15 also has only one "✓", so m(10,11,14,15) is also essential. Now all columns with one "✓" are covered. The rows with minterm m(4,12) and m(10,11,14,15) can now be removed, together with all the columns they cover.

The second prime implicant can be 'covered' by the third and fourth, and the third prime implicant can be 'covered' by the second and first, and neither is thus essential. If a prime implicant is essential then, as would be expected, it is necessary to include it in the minimized boolean equation. In some cases, the essential prime implicants do not cover all minterms, in which case additional procedures for chart reduction can be employed. The simplest "additional procedure" is trial and error, but a more systematic way is [[Petrick's method]]. In the current example, the essential prime implicants do not handle all of the minterms, so, in this case, the essential implicants can be combined with one of the two non-essential ones to yield one equation:

:''f''{{sub|A,B,C,D}} = BC'D' + AB' + AC<ref name="Logic_Friday"/>
or
:''f''{{sub|A,B,C,D}} = BC'D' + AD' + AC

Both of those final equations are functionally equivalent to the original, verbose equation:
:''f''{{sub|A,B,C,D}} = A'BC'D' + AB'C'D' + AB'C'D + AB'CD' + AB'CD + ABC'D' + ABCD' + ABCD.