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9.10
Assume numbers are represented in 8-bit twos complement representation. Show the calculation of the following:
Assume numbers are represented in 8-bit twos complement representation. Show the calculation of the following:
a. 6+13 = 00000110 + 00001101 = 00011011
b. -6+13 = 11111010 + 00001101 = (1)00000111
c. 6-13 = 00000110 + 11110011 = 11111001
d. -6-13 = 11111010 + 11110011 = (1)11101101
9.11
Find the following differences using twos complement arithmetic
Find the following differences using twos complement arithmetic
a. 111000
-110011
111000
+001101
=(1)000101
b. 11001100
- 101110
101110 = 010010
11001100
+ 010010
=11011110
c. 111100001111
-110011110011
110011110011 = 001100001101
111100001111
+ 001100001101
=(1)001000011100
d. 11000011
-11101000
11101000 = 00011000
11000011
+ 00011000
= 11011011
9.23
Express the following numbers in IEEE 32-bit floating point format:
Express the following numbers in IEEE 32-bit floating point format:
a. -5
5 = 101 = 1.01 x 22
exponent = 127 + 2 = 129 = 10000001
1 10000001 01000000000000000000000
b. -6
6 = 110 = 1.10 x 22
exponent = 127 + 2 = 129 = 10000001
1 10000001 10000000000000000000000
c. -1.5
1.5 = 1.1 = 1.1 x 20
exponent = 127 = 01111111
1 01111111 10000000000000000000000
d. 384
384 = 384-256 = 128 -128 = 0; = 110000000 = 1.1 x 28
exponent = 8 + 127 = 135 = 10000111
0 10000111 10000000000000000000000
e. 1/16
1/16 = .0001 = 1.0 x 2-4
exponent = 127 – 4 = 123 = 01111011
0 01111011 00000000000000000000000
f. -1/32
1/32 = .00001 = 1.0 x 2-5
exponent = 127 – 5 = 122 = 01111010
1 01111010 00000000000000000000000
9.24
The following numbers use the IEEE 32-bit floating-point format. What is the equivalent decimal value?
The following numbers use the IEEE 32-bit floating-point format. What is the equivalent decimal value?
a. 1 10000011 11000000000000000000000
sign = -
exponent = 131 – 127 = 4
1.11 x 24 = 11100 = 28
-28
b. 0 01111110 10100000000000000000000
sign = +
exponent = 126 – 127 = -1
1.101 x 2-1 = .1101 = ½ + ¼ + 1/16 = .8125
.8125
c. 0 10000000 00000000000000000000000
sign = +
exponent = 128 – 127 = 1
1.0 x 21 = 10 = 2
2
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