SP12-CSE20 Discrete Mathematics
Homework 1 Solution
April 17, 2012
1 Boolean Functions and Computer Arith-
metic
1.1 Problem 2.12
Find the 8-bit two’s complement of 6710.
We first convert it into binary format then calculate its two’s comple-
ment. We iteratively divide this decimal number by 16 and set each digit
(from lowest to highest) to be the remainder. For instance, 6710/2 = 33 and
6710 mod 2 = 1, so the first bit is set to be 1, and we replace 67 with 33
for the following division and modulation operations. In the end the binary
number is 1000011, which is only of 7 bits, so we add 0 to the high-end bit
and make it to be 01000011. The two’s complement is thus obtained by flip
all the bits then add it by 1, which turns out to be 10111101.
1.2 Problem 2.13
Find the 8-bit two’s complement of 10810.
As above, we first convert it into binary format then calculate its two’s
complement. We iteratively divide this decimal number by 16 and set each
digit (from lowest to highest) to be the remainder. For instance, originally
for the first iteration, we have 10810/2 = 54 and 10810 mod 2 = 0, so the
first bit is set to be 10, and we replace 108 with 54 for the following division
and modulation operations. In the end the binary number becomes 1101100,
which is only of 7 bits, so we add 0 to the high-end bit and make it to be
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