use the properties and theorems of boolean algebra to reduce the following expre
ID: 3556676 • Letter: U
Question
use the properties and theorems of boolean algebra to reduce the following expresssions to AND-OR expressions without parentheses. The expressions may not be unique. Construct the truth table, which will be unique, by inspection of your final expression.
(ab(+)b')' +ab (the (+) is the circle with a plus inside it)
use the properties and theorems of boolean algebra to reduce the following expresssions to OR-AND expressions without parentheses. The expressions may not be unique. Construct the truth table, which will be unique, by inspection of your final expression.
ab+a'b'
Explanation / Answer
(ab(+)b')' +ab = (ab.b + (ab)'b')' + ab ( using a(+)b = ab' + a'b)
= ( ab + (a'+b')b')' + ab (using (ab)' = a'+b' and b.b = b)
= (ab + a'b' + b')' + ab ( using b'.b' = b')
= (ab)'(a'b')'b + ab ( using (a+b+c)' = a' + b' + c')
= (a'+b')(a+b)b + ab (using (ab)' = a'+b')
= (a.a' + a'.b + b'.a + b'.b) b + ab
= (a'b + b'a)b + ab (using a.a' = 0)
= (a'b + b'a + a)b
= (a'b + a)b ( using 1+b' = 1)
= a'b + ab (using b.b = b)
= b ( using a'+a = 1)
the truth table is as follows:
ab+a'b' nothing to reduce
the truth table is
The final expression is same as the given expression
a b ab b' ab(+)b' (ab(+)b')' (ab(+)b')' +ab final 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1Related Questions
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