Spring 2000
Computer Science 3410 - Solutions
Combinational Logic
Design a combinational circuit that adds one to a 4-bit binary number, A
3
A
2
A
1
A
0
. For example, if the input of the circuit is A
3
A
2
A
1
A
0
= 1101, the output is 1110. The circuit can be designed using four half-adders.
A combinational circuit produces the binary sum of two 2-bit numbers, x
1
x
0
and y
1
y
0
. The outputs are C, S
1
, and S
0
. Provide a truth table of the circuit.
Design the above circuit using two full-adders.
Derive the truth table of the circuit shown below.
Draw the NAND logic diagram for each of the following expressions using multiple-level NAND gate circuits:
a) (AB' + CD')E + BC(A + B)
b) w(x + y + z) + xyz
Verify that the circuit below generates the exclusive-NOR function.
Prove that x'
y = x
y' = (x
y)' = xy + x'y'
Prove that x
1 = x' and x
0 = x
Design a circuit of a 3-bit parity generator and the circuit of a 4-bit parity checker using an odd parity bit.
