2.
Design a combinational circuit that adds two binary numbers
x
and
y
and produces
two binary numbers
C
(for carry) and
S
(for sum). This circuit is called a half adder.
(a)
Construct a truth table of the half adder.
(b)
Using Karnaugh maps, obtain simplest SOP expressions for
C
and
S
.
(c)
Implement the half adder using AND and OR gates only and draw a logic diagram.
You may assume doublerail logic.
(d)
Implement the half adder using an XOR gate and an AND gate only and draw a logic
diagram.
3.
Show algebraically that a full adder can be realized by two half adders and an OR gate.
Then draw a logic diagram.
Assume that the full adder has three inputs
x
,
y
, and
c
in
and two
outputs
c
out
and
s
.
4.
Design a combinational circuit that multiplies two 2bit numbers,
a
1
a
0
and
b
1
b
0
, to
produce a 4bit product,
c
3
c
2
c
1
c
0
.
(a)
Construct the truth table.
(b)
Derive a simplest Boolean function in SOP form for each output.
(c)
Realize the circuit using AND gates and half adders. Draw a logic diagram.
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 Spring '08
 PETROV
 Boolean Algebra, Binary numeral system, Logic gate, Binarycoded decimal, Logical connective, logic diagram

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