Question

Implement the following functions using logic gates. Assume that the compliments of each variable are available.

a. F(A,B,C,D) = (AB)’(C+D’)

b. F(A,B,C) = AB’+ A’B+ CB

c. F(A,B,C,D) = (A’+B’)’+CD + C’D’

d. F(A,B,C) = ((A+B)’(A’+B))’

Answer 1

(a) F(A,B,C,D)=(AB)'(C+D')

CIRCUIT DIAGRAM (4 inputs, 1 output)

(In these diagrams the logic gate numbers have no significance in relation to the question.)

(b) F(A,B,C)=AB'+A'B+CB (3 inputs, 1 output)

CIRCUIT DIAGRAM

(c) F(A,B,C,D)=(A'+B')'+C'D'+CD (4 inputs, 1 output)

(A'+B')'+C'D'+CD is the same as (A'+B')'+CD+C'D')

CIRCUIT DIAGRAM

(d) F(A,B,C)=((A+B)'(A'+B))' (3 inputs, 2 outputs)

CIRCUIT DIAGRAM

System size limitations have caused me to revise the presentation of this solution, so truth tables for each part of the question have been prepared as a single unit, shown below. (Signal convention is 1=ON, 0=OFF for the inputs and outputs.)