ganutenator
Lifetime Supporting Member
Example:
Take this boolean algebraic expression:
note: I'm using a single quote to denote negation as I can't place a bar over the letter.
(CA + B' + C + D') * C
When you reduce this expression:
1) CA + CB' + C*C + CD' // multiply C by what is in parens
2) CA + CB' + C + CD' // we replace (C * C) with C because: C * C = C because: C AND C = C
3) CA + CB' + C * (1 + D') // we factor out C from (C + CD').
4) CA + CB' + C * 1 // (1 + D') = 1 because: (1 OR NOT D) = 1
5) CA + CB' + C // because: C * 1 = C or C AND 1 = C
6) CA + C * (B' + 1) // we know that (B' + 1) = 1 because NOT B OR 1 = 1
7) CA + C * 1
8) CA + C // (C * 1) = C because C AND 1 = C
9) C * (A + 1) // (A + 1) also known as A OR 1 = 1
10) C * 1 // C AND 1 = C
= C
Not immediately apparent that (A + B' + C + D') * C = C
Now in ladder as (CA + CB' + CC + CD'):
Take this boolean algebraic expression:
note: I'm using a single quote to denote negation as I can't place a bar over the letter.
(CA + B' + C + D') * C
When you reduce this expression:
1) CA + CB' + C*C + CD' // multiply C by what is in parens
2) CA + CB' + C + CD' // we replace (C * C) with C because: C * C = C because: C AND C = C
3) CA + CB' + C * (1 + D') // we factor out C from (C + CD').
4) CA + CB' + C * 1 // (1 + D') = 1 because: (1 OR NOT D) = 1
5) CA + CB' + C // because: C * 1 = C or C AND 1 = C
6) CA + C * (B' + 1) // we know that (B' + 1) = 1 because NOT B OR 1 = 1
7) CA + C * 1
8) CA + C // (C * 1) = C because C AND 1 = C
9) C * (A + 1) // (A + 1) also known as A OR 1 = 1
10) C * 1 // C AND 1 = C
= C
Not immediately apparent that (A + B' + C + D') * C = C
Now in ladder as (CA + CB' + CC + CD'):