Editing Canonical normal form (section)

===Minterm canonical form===

Given the [[truth table]] of a logical function, it is possible to write the function as a "sum of products" or "sum of minterms". This is a special form of [[disjunctive normal form]]. For example, if given the truth table for the arithmetic sum bit ''u'' of one bit position's logic of an adder circuit, as a function of ''x'' and ''y'' from the addends and the carry in, ''ci'':

{| class="wikitable" style="margin: 1em auto 1em auto"
!width="50"|ci
!width="50"|x
!width="50"|y
!width="50"|u(ci,x,y)
|-
|0||0||0||0
|-
|0||0||1||1
|-
|0||1||0||1
|-
|0||1||1||0
|-
|1||0||0||1
|-
|1||0||1||0
|-
|1||1||0||0
|-
|1||1||1||1
|}

Observing that the rows that have an output of 1 are the 2nd, 3rd, 5th, and 8th, we can write ''u'' as a sum of minterms <math>m_1, m_2, m_4,</math> and <math>m_7</math>. If we wish to verify this: <math> u(ci,x,y) = m_1 + m_2 + m_4 + m_7 = (ci',x',y)+(ci',x,y') + (ci,x',y')+(ci,x,y)</math> evaluated for all 8 combinations of the three variables will match the table.