Computer Science 161.02
Digital Circuit Design (Homework #4)
Monday September 22nd 2014
May be done in pairs.
Name(s): ______________________________________________________________
1. A Circuit to Test
Equality: Create
a circuit with inputs a1, b1, a2, b2
which will output 1 if and only if, as two-bit numbers, a1b1=a2b2.
Create and simulate the circuit using this
software. Draw the circuit in the
space provided below.
2. Half-Adder
Circuit: Create
the Half-Adder (HA) circuit that we just derived in class, using this software.
Test the circuit with all 4 possible input combinations. Record the results in the truth table below.
Carefully draw the circuit.
a b sum carry-out
0 0
0
1
1
0
1 1
3. Full adder circuit: A full adder circuit is one that performs the
addition that occurs in
any column other than the rightmost. For this, we’ll require three inputs
(carry-in, a, b)
and, once again, two outputs (sum and carry-out). We want to make liberal use of
XOR gates, and note the
following: that adding three bits is really done
as follows: first “adding” two bits and then “adding”
that result to the third. For now,
draw only that part of the circuit that computes the sum
bit and we’ll worry about the
carry-out bit later.
Test the sum part by testing all 8 combinations of the 3 inputs and
filling in the truth table for sum.
Carry-in a b sum carry-out
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
The carry-out logic can be
thought of as follows – a carry-out occurs whenever a and b
are both 1, but also whenever the carry-in is 1 and exactly
one of a and b is 1. (See if that
makes sense after filling out the column for carry-out
above). This logic can be
expressed as follows:
carry-out = (a
AND b) OR (carry-in AND (a XOR b))
Create the entire full-adder
circuit and carefully draw it on a blank sheet of
paper.
Think about how a
full-adder might be constructed from two half-adders.