S 31 a) Show the IEEE 754 binary representation for the floating-point number 1024.8125 in single precision. 30 29 28 Exponent 27 28 29 30 3 2¹1 21⁰ 2⁹ 2² 27 128 in 2048 1024 512 256 22 25 64 21 20 19 18 17 16 2³ 24 32 16 2³ 2² 2² 8 4 2 Fraction 13 2⁰ 1 12 11 2-¹ 2-² 2-3 05 0.25 2-4 0.125 0.0625 2-5 2-6 0.03125 0.015625
S 31 a) Show the IEEE 754 binary representation for the floating-point number 1024.8125 in single precision. 30 29 28 Exponent 27 28 29 30 3 2¹1 21⁰ 2⁹ 2² 27 128 in 2048 1024 512 256 22 25 64 21 20 19 18 17 16 2³ 24 32 16 2³ 2² 2² 8 4 2 Fraction 13 2⁰ 1 12 11 2-¹ 2-² 2-3 05 0.25 2-4 0.125 0.0625 2-5 2-6 0.03125 0.015625
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
![S
31
0
S
31
a) Show the IEEE 754 binary representation for the floating-point number 1024.8125 in single precision.
Exponent
30 29 28 27 26 25 24 23 22 21 20 19
2¹¹ 21⁰ 2⁹ 2² 27 25 2³
2048 1024 512 256 128 64
30 29 28
211
2048
0 1 0
210
1024
1 1
O
24
32 16
1 0
2⁹ 2² 27 25
512 256 128
64
21 20
1 0
19
b) What is this single precision floating point number using IEEE 754 encoding in decimal notation?
Exponent
27 26 25 24 23 22
24
1 1
2³
32 16
N
18 17
2³ 2²
00
AN
4
18 17 16 15 14 13
2³
8
000
00
14
AN
Fraction
2² 2⁰
2
1
4
13
ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܪ
2² 2²
2
2-¹ 2-² 2-3³
2-4
2-5
0.5 0.25 0.125 0.0625 0.03125
Fraction
10
12 11 10 9
2⁰
1
2-²
0.5
8
7
00 00
2-² 2-³ 2-4
2-5
0.25 0.125 0.0625 0.03125
A
ܘ ܘ ܘ ܘ ܝ
0
2-6
0.015625
1
2-6
0.015625](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd85baa52-0289-4b87-9e7c-1bb16856cc21%2Ffb26a4bc-c7ca-44dd-b663-89b586d2f315%2F3pbbrkk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:S
31
0
S
31
a) Show the IEEE 754 binary representation for the floating-point number 1024.8125 in single precision.
Exponent
30 29 28 27 26 25 24 23 22 21 20 19
2¹¹ 21⁰ 2⁹ 2² 27 25 2³
2048 1024 512 256 128 64
30 29 28
211
2048
0 1 0
210
1024
1 1
O
24
32 16
1 0
2⁹ 2² 27 25
512 256 128
64
21 20
1 0
19
b) What is this single precision floating point number using IEEE 754 encoding in decimal notation?
Exponent
27 26 25 24 23 22
24
1 1
2³
32 16
N
18 17
2³ 2²
00
AN
4
18 17 16 15 14 13
2³
8
000
00
14
AN
Fraction
2² 2⁰
2
1
4
13
ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܘ ܪ
2² 2²
2
2-¹ 2-² 2-3³
2-4
2-5
0.5 0.25 0.125 0.0625 0.03125
Fraction
10
12 11 10 9
2⁰
1
2-²
0.5
8
7
00 00
2-² 2-³ 2-4
2-5
0.25 0.125 0.0625 0.03125
A
ܘ ܘ ܘ ܘ ܝ
0
2-6
0.015625
1
2-6
0.015625
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