A computer uses 8-bit for FLP (1 bit for sign, 4 bit for exponent with excess-7
ID: 3900790 • Letter: A
Question
A computer uses 8-bit for FLP (1 bit for sign, 4 bit for exponent with excess-7 rep. (see table below), rest for magnitude). Assume 0000 and 1111 in exponent field are reserved for denormalization.
Decimal
0
1
2
3
4
5
6
7
Unsigned
0000
0001
0010
0011
0100
0101
0110
0111
Excess-7
Reserved
-6
-5
-4
-3
-2
-1
0
Decimal
8
9
10
11
12
13
14
15
Unsigned
1000
1001
1010
1011
1100
1101
1110
1111
Excess-7
1
2
3
4
5
6
7
reserved
a. What is 11000000?
1
1000
000
Answer: - 1.0 * 2 ^ 1 = - 2
b. How 1 will be represented?
Answer:
c. What is the smallest fraction in this representation? (normalized)
min +ve
d. What is the largest number?
Largest
e. What is the second largest number?
second largest
f. Show that 240 -5 = 240 in this representation.
Decimal
0
1
2
3
4
5
6
7
Unsigned
0000
0001
0010
0011
0100
0101
0110
0111
Excess-7
Reserved
-6
-5
-4
-3
-2
-1
0
Explanation / Answer
a) The Value of 11000000 is 1 1000 000 = -1.000x 2 ^ 1 = -2 in decimal.
b) 1 is a positive number so MSB is 0. now write it in binary which is 0000 0001 make it in scintific format
1.0X 2 ^ 0 so add 7 for the exponent = 0 + 7 = >7 = 0111 and our exponent is 0111 and our mantissaa is 000
so final representation is 0 0111 000 = 00111000 in binary
c) The smallest fraction of a negative number is MSB 1 and all zeros in the mantissa 10000000 which is 1 0000 000
and it will be equal to -1.000 X 2 ^ (0-7) = -1.0X 2 ^-7 = -0.0078 in decimal
and the smallest positive number will 00000000 which is 0 0000 000 and it will 1.0 X 2 ^ -7 = 0.0078
d) The largest number will be 01111111 which is 0 1111 111
and it will equal lto 1.111 X 2 ^ (15-7) = 1.111X 2 ^ 8 = 111100000 = 480 in decimal
e) the Second largest number will 01111110 which is 0 1111 110
and it will equal to 1.110 X 2 (15-7) = 1.110 X 2 ^ 8= 111000000 = 448 in decimal
f)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.