BLG 231E - Digital Circuits
Assignment 2
1. The truth table for a function y(A, B, C, D) is given below:
A B C D y
0 0 0 0 0 0
1 0 0 0 1 1
2 0 0 1 0 0
3 0 0 1 1 1
4 0 1 0 0 0
5 0 1 0 1 1
6 0 1 1 0 0
7 0 1 1 1 0
8 1 0 0 0 0
9 1 0 0 1 1
10 1 0 1 0 1
11 1 0 1 1 0
12 1 1 0 0 1
13 1 1 0 1 0
14 1 1 1 0 1
15 1 1 1 1 1
a. Write the expressions of y in the first and second canonical forms.
b. Minimize the expression in the first canonical form using axioms and theorems of Boolean algebra.
Show all steps in your minimization and write the name of the axiom/theorem/property you use on
the right-hand side of the expression at each step.
c. Draw the circuit for the minimized expression in (b) using 2-input NAND gates only. Show all steps
and explain your work leading up to the final circuit.
