Combinational circuits Design Questions and Answers

ICT Questions and Answers

Question 1
A digital circuit takes four digits as an input, and produce 'X' as its output. If the decimal value represented by the four binary digit is a prime number. If it is prime output is 1 otherwise 0. Assume that all four binary digit represent positive decimal values.

i) Draw a truth table for the above problem.
ii) Write the Boolean expression in the sum of product form.
iii) Design a logic circuit for the Boolean expression, which is obtained above.
iv) Simplify the expression using Boolean algebra/ Karnaugh map.

Answer
i) Truth Table

A	B	C	D	X
0	0	0	0	0
0	0	0	1	0
0	0	1	0	1
0	0	1	1	1
0	1	0	0	0
0	1	0	1	1
0	1	1	0	0
0	1	1	1	1
1	0	0	0	0
1	0	0	1	0
1	0	1	0	0
1	0	1	1	1
1	1	0	0	0
1	1	0	1	1
1	1	1	0	0
1	1	1	1	0

ii) X= A'B'CD' + A'B'CD + A'BC'D + A'BCD + AB'CD + ABC'D

iii)

iv)

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Question 2
Consider the logic circuit shown here to answer the below questions.

i) Write and simplify the Boolean expression for the above circuit using Boolean algebra . Show all the workings and algebraic rules used for the simplification.

ii) Construct the logic circuit using combination of only AND, OR and NOT gates for the simplified Boolean expression obtained above.

Answer
i)
ABC + A'BC + ABC'
BC(A+A') + ABC'
BC + ABC'
B(C+AC')
B(A+C)

ii)