Editing Quine–McCluskey algorithm (section)

===Step 1: Finding the prime implicants===
First, we write the function as a table (where 'x' stands for don't care):
:{| class="wikitable"
|-
!   !! A !! B !! C !! D !! f
|-
| m0 || 0 || 0 || 0 || 0 || 0
|-
| m1 || 0 || 0 || 0 || 1 || 0
|-
| m2 || 0 || 0 || 1 || 0 || 0
|-
| m3 || 0 || 0 || 1 || 1 || 0
|-
| m4 || 0 || 1 || 0 || 0 || 1
|-
| m5 || 0 || 1 || 0 || 1 || 0
|-
| m6 || 0 || 1 || 1 || 0 || 0
|-
| m7 || 0 || 1 || 1 || 1 || 0
|-
| m8 || 1 || 0 || 0 || 0 || 1
|-
| m9 || 1 || 0 || 0 || 1 || x
|-
| m10 || 1 || 0 || 1 || 0 || 1
|-
| m11 || 1 || 0 || 1 || 1 || 1
|-
| m12 || 1 || 1 || 0 || 0 || 1
|-
| m13 || 1 || 1 || 0 || 1 || 0
|-
| m14 || 1 || 1 || 1 || 0 || x
|-
| m15 || 1 || 1 || 1 || 1 || 1
|}

One can easily form the canonical [[sum of products]] expression from this table, simply by summing the [[minterm]]s (leaving out [[Don't-care (logic)|don't-care terms]]) where the function evaluates to one:

:''f''{{sub|A,B,C,D}} = A'BC'D' + AB'C'D' + AB'CD' + AB'CD + ABC'D' + ABCD.

which is not minimal. So to optimize, all minterms that evaluate to one are first placed in a minterm table. Don't-care terms are also added into this table (names in parentheses), so they can be combined with minterms:

:{| class="wikitable"
|-
! Number<br/>of 1s !! Minterm !! Binary<br/>Representation
|-
| rowspan="2" | 1
| m4 || {{mono|0100}}
|-
| m8 || {{mono|1000}}
|-
| rowspan="3" | 2
| (m9) || {{mono|1001}}
|-
| m10 || {{mono|1010}}
|-
| m12 || {{mono|1100}}
|-
| rowspan="2" | 3
| m11 || {{mono|1011}}
|-
| (m14) || {{mono|1110}}
|-
|| 4
| m15 || {{mono|1111}}
|}

At this point, one can start combining minterms with other minterms in adjacent groups; as in, we compare minterms in nth group with (n+1)th group. So for the m4 minterm in with only one Number of 1s, we compare it to m9, m10, and m12 which have two Number of 1s.

If two terms differ by only a single digit, that digit is replaced with a dash indicating that the digit doesn't matter. For instance <code>1000</code> and <code>1001</code> can be combined to give <code>100-</code>, indicating that both minterms imply the first digit is <code>1</code> and the next two are <code>0</code>. Terms that can't be combined any more are marked with an asterisk ({{color|red|*}}).

:{| class="wikitable"
|-
! Number<br/>of 1s !! Minterm !! 0-Cube !! colspan="2" | Size 2 Implicants 
|-
| rowspan="4" | 1
| m4 || {{mono|0100}} || m(4,12) || {{mono|-100 {{color|red|*}}}}
|-
| m8 || {{mono|1000}} || m(8,9) || {{mono|100-}}
|-
| colspan="2" {{sdash}} || m(8,10) || {{mono|10-0}}
|-
| colspan="2" {{sdash}} || m(8,12) || {{mono|1-00}}
|-
| rowspan="4" | 2
| m9 || {{mono|1001}} || m(9,11) || {{mono|10-1}}
|-
| m10 || {{mono|1010}} || m(10,11) || {{mono|101-}}
|-
| colspan="2" {{sdash}} || m(10,14) || {{mono|1-10}}
|-
| m12 || {{mono|1100}} || m(12,14) || {{mono|11-0}}
|-
| rowspan="2" | 3
| m11 || {{mono|1011}} || m(11,15) || {{mono|1-11}}
|-
| m14 || {{mono|1110}} || m(14,15) || {{mono|111-}}
|-
| rowspan="1" | 4
| m15 || {{mono|1111}} || colspan="2" {{sdash}}
|}

When going from Size 2 to Size 4, treat <code>-</code> as a third bit value. Match up the <code>-</code>'s first.  The terms represent products and to combine two product terms they must have the same variables. One of the variables should be complemented in one term and uncomplemented in the other. The remaining variables present should agree. So to match two terms the <code>-</code>'s must align and all but one of the other digits must be the same. For instance, <code>-110</code> and <code>-100</code> can be combined to give <code>-1-0</code>, as can <code>-110</code> and <code>-010</code> to give <code>--10</code>, but <code>-110</code> and <code>011-</code> cannot since the <code>-</code>'s do not align. <code>-110</code> corresponds to BCD' while 
<code>011-</code> corresponds to A'BC, and BCD' + A'BC is not equivalent to a product term.
:{| class="wikitable"
|-
! Number<br/>of 1s !! Minterm !! 0-Cube !! colspan="2" | Size 2 Implicants !! colspan="2" | Size 4 Implicants
|-
| rowspan="4" | 1
| m4 || {{mono|0100}} || m(4,12) || {{mono|-100 {{color|red|*}}}} ||colspan="2" {{sdash}}
|-
| m8 || {{mono|1000}} || m(8,9) || {{mono|100-}} || m(8,9,10,11) || {{mono|10-- {{color|red|*}}}}
|-
| colspan="2" {{sdash}} || m(8,10) || {{mono|10-0}} || m(8,10,12,14)  || {{mono|1--0 {{color|red|*}}}}
|-
| colspan="2" {{sdash}} || m(8,12) || {{mono|1-00}} ||colspan="2" {{sdash}}
|-
| rowspan="4" | 2
| m9 || {{mono|1001}} || m(9,11) || {{mono|10-1}} ||colspan="2" {{sdash}}
|-
| m10 || {{mono|1010}} || m(10,11) || {{mono|101-}} || m(10,11,14,15) || {{mono|1-1- {{color|red|*}}}}
|-
| colspan="2" {{sdash}} || m(10,14) || {{mono|1-10}} ||colspan="2" {{sdash}}
|-
| m12 || {{mono|1100}} || m(12,14) || {{mono|11-0}} ||colspan="2" {{sdash}}
|-
| rowspan="2" | 3
| m11 || {{mono|1011}} || m(11,15) || {{mono|1-11}} ||colspan="2" {{sdash}}
|-
| m14 || {{mono|1110}} || m(14,15) || {{mono|111-}} ||colspan="2" {{sdash}}
|-
| rowspan="1" | 4
| m15 || {{mono|1111}} || colspan="2" {{sdash}}
| colspan="2" {{sdash}}
|}

Note: In this example, none of the terms in the size 4 implicants table can be combined any further. In general, this process is continued in sizes that are powers of 2 (sizes 8, 16 etc.) until no more terms can be combined.