EECE 2322 Fall 2023 Prof. Leeser Homework 1
1. A three input logic gate has inputs A, B and C. If input A and input C are both 1, the output is 0. In
all other cases, the output is 1.
a) Write a truth table for this three input gate.
b) Write a Boolean equation for this logic gate using AND, OR and NOT.
c) Draw an implementation of the 3 input gate using NAND gates only.
2. A half subtractor has inputs X and Y and outputs D (difference) and B (borrow). If X and Y are the
same, both D and B are 0. If X is 1 and Y is 0, the difference is 1 but there is no borrow. If X is 0 and Y is
1, there is both a difference and a borrow.
a) Write a truth table for the half subtractor.
b) Write Boolean equations for the half subtractor using AND, OR, XOR, and NOT gates.
c) Draw an implementation of the half subtractor using AND, OR, XOR, and NOT gates.
3. A full subtractor taxes in 3 inputs, X, Y and B_in, and generates two outputs D and B_out. Its truth
table is:
B_in
0
0
0
0
1
1
1
1
Y
0
0
1
1
0
0
1
1
X
0
1
0
1
0
1
0
1
D
0
1
1
0
1
0
0
1
B_out
0
0
1
0
1
0
1
1
a) Write Boolean equations for the full subtractor using AND, OR, XOR, and NOT.
b) Draw an implementation of the full subtractor using AND, OR, XOR, and NOT gates.
c) Draw an implementation of the full subtractor using half subtractors and any additional logic gates
that you need.
4. Simplify the Boolean equations shown below. Draw a simple circuit for each of these equations.
5. A truth table has 4 Giga rows. How many input variables are there?