B.27 [15] <§B.6> Write the equations for the carry- lookahead logic for a 64-bit adder using the new
B.27 [15] <§B.6> Write the equations for the carry- lookahead logic for a 64-bit adder using the new
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
# B.29
Transcribed Image Text:Carryln
a0
b0
a1
b1
Carryln
Result0-3
a2
ALUO
b2
pi
gi
PO
a3
b3
GO
C1
ci + 1
Carry-lookahead unit
a4
b4
Carryln
Result4–7
a5
b5
ALU1
a6
b6
P1
pi + 1
a7
G1
gi + 1
b7
C2
ci + 2
a8
b8
a9
b9
Carryln
Result8–11
ALU2
a10
b10
pi +2
gi + 2
P2
a11
G2
b11
C3
ci + 3
a12-
b12
Carryln
Result12–15
а13
b13
a14
b14
a15
b15
ALU3
pi + 3
gi + 3
P3
G3
C4
ci + 4
CarrvOut
![B.27 [15] <§B.6> Write the equations for the carry-
lookahead logic for a 64-bit adder using the new
notation from Exercise B.26 and using 16-bit adders as
building blocks. Include a drawing similar to Figure
B.6.3 in your solution.
B.28 [10] <$B.6> Now calculate the relative
performance of adders. Assume that hardware
corresponding to any equation containing only OR or
AND terms, such as the equations for pi and gi on page
B-40, takes one time unit T. Equations that consist of
the OR of several AND terms, such as the equations for
c1, c2, c3, and c4 on page B-40, would thus take two
time units, 2T. The reason is it would take T to produce
the AND terms and then an additional T to produce the
result of the OR. Calculate the numbers and
performance ratio for 4-bit adders for both ripple carry
and carry lookahead. If the terms in equations are
further defined by other equations, then add the
appropriate delays for those intermediate equations,
and continue recursively until the actual input bits of
the adder are used in an equation. Include a drawing
of each adder labeled with the calculated delays and
the path of the worst-case delay highlighted.
B.29 [15] <§B.6> This exercise is similar to Exercise
B.28, but this time calculate the relative speeds of a
16-bit adder using ripple carry only, ripple carry of 4-
bit groups that use carry lookahead, and the carry-
lookahead scheme on page B-39.
D 20 r151
Thi](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5455ed20-575a-4ee0-b183-314110c53f0d%2F0e66bb5b-961e-4820-a85d-c8149af4d01b%2F1jzrjq_processed.png&w=3840&q=75)
Transcribed Image Text:B.27 [15] <§B.6> Write the equations for the carry-
lookahead logic for a 64-bit adder using the new
notation from Exercise B.26 and using 16-bit adders as
building blocks. Include a drawing similar to Figure
B.6.3 in your solution.
B.28 [10] <$B.6> Now calculate the relative
performance of adders. Assume that hardware
corresponding to any equation containing only OR or
AND terms, such as the equations for pi and gi on page
B-40, takes one time unit T. Equations that consist of
the OR of several AND terms, such as the equations for
c1, c2, c3, and c4 on page B-40, would thus take two
time units, 2T. The reason is it would take T to produce
the AND terms and then an additional T to produce the
result of the OR. Calculate the numbers and
performance ratio for 4-bit adders for both ripple carry
and carry lookahead. If the terms in equations are
further defined by other equations, then add the
appropriate delays for those intermediate equations,
and continue recursively until the actual input bits of
the adder are used in an equation. Include a drawing
of each adder labeled with the calculated delays and
the path of the worst-case delay highlighted.
B.29 [15] <§B.6> This exercise is similar to Exercise
B.28, but this time calculate the relative speeds of a
16-bit adder using ripple carry only, ripple carry of 4-
bit groups that use carry lookahead, and the carry-
lookahead scheme on page B-39.
D 20 r151
Thi
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