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Quiz 2
EECS 427: VLSI Design I
CLOSED BOOK, CLOSED NOTES!!
Underlined text
highlights the specific questions you need to answer.
1. Arithmetic units [29 points total]
a) A portion of example 11.5 from the Rabaey text is shown below.
There is a minor
error in the example – find this error
.
[4 points]
Example 11.5: Modified Booth’s Recoding
Consider the 8bit binary number 01111110 shown earlier.
This can be divided
into four overlapping groups of three bits, going from
msb
to
lsb
: 00(1), 11(1),
11(1), 10(0).
b) Perform twos complement binary multiplication
of 6 times 7 using a 4bit
multiplicand and multiplier.
Use modified booth recoding on the multiplier which is 7
in this case.
[15 points]
c) The use of a log shifter with base 4 instead of 2 is helpful in reducing the number
of series connected pass transistors in shifters with potentially large shift amounts.
A drawback is the need to reencode the shift amount, whereas in log
2
shifters this
information is already encoded properly.
For a 16bit log
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 Spring '12
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