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Digital Logic Homework
University of Information Technology

Computer Engineering Faculty
Page 1
Homework6
(Due November 08, 2010)
1.
In the equation below, the function
greater_than
(
x
3
x
2
x
1
x
0
,
z
3
z
2
z
1
z
0
)
is true, if and only if, the numerical value represented by
x
3
x
2
x
1
x
0
is
greater than the numerical value represented by
z
3
z
2
z
1
z
0
. Similarly
for the
equal
function. Explain why this equation is true.
Use this equation to design a 4 bit comparison circuit consisting of
four copies of a single subcircuit. Your circuit should have three
outputs
X
>
Z
,
X=Z
and
X
<
Z
, where the first output is high if the
numerical value represented by inputs
x
3
x
2
x
1
x
0
is greater than the
numerical value represented by inputs
z
3
z
2
z
1
z
0
, and so forth.
Assuming a 1 ns gate delay on all gates in your design, what is the
circuit’s worstcase propagation delay?
2.
The logic diagram below shows a 5 bit ripplecarry decrement
circuit. Draw a logic diagram for a 5 bit borrowlookahead
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