logic gates

Question

Hey! is there a shortcut to finding the number of gates to be used in similar questions? I am unable to solve these questions. Please help.

Comments

when we put the value in truth table

A   B   C     f(A,B,C )

0  0    0      0

0 0   1         0

0 1    0       0

0   1    1      1

1   0    0      1

1  0  1          1

1  1   0         1

1   1   1       1

f(A,B,C)=sigm   m (3,4,5,6,7)

after minimization this should be equal to A+BC

so one  OR AND one AND gate required

Answer 1

$\underline{\text{Simplification}}:$

$A \oplus B \oplus AB = A \oplus (B \oplus AB) = A \oplus B \ (1 \oplus A) = A \oplus B \bar{A} \equiv A + B \bar{A} = A + B $ 

$A \oplus C \oplus AC = A \oplus (C \oplus AC) = A \oplus C \ (1 \oplus A) = A \oplus C \bar{A} \equiv A + C \bar{A} = A + C $ 

 

$\text{So, (A+B)(A+C) = A + BC  i.e  1 AND Gate & 1 OR Gate required}$ 

 

$\text{Circuit Diagram:}$ CLICK HERE