S31a) Show the IEEE 754 binary representation for the floating-point number 1024.8125 in single precision.Exponent30 29 28 27 26 25 24 23 2221 20 19 18 17 16211 210 2⁹ 28 27 26 25 242048 1024 512 256 128 6432 16Fraction15 14 13 12 11 10 92³ 2² 2¹ 2⁰ 2-1 2.-²84202-3 2-4 2-5 2-60.0625 0.03125 0.0156251 0.5 0.25 0.125

In computer science and numerical representation, a floating-point number format specified by the…

a) Show the IEEE 754 binary representation for the floating-point number 1024.8125 in single precision. S Exponent Fraction 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 211 210 2⁹ 28 27 26 25 24 2³ 2048 1024 512 256 128 64 32 16 8 2² ~ 4 2¹ 2⁰ 21 22 23 24 2.5 2-6 2 1 0.5 0.25 0.125 0.0625 0.03125 0.015625 N

a) Show the IEEE 754 binary representation for the floating-point number 1024.8125 in single precision. S Exponent Fraction 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 211 210 2⁹ 28 27 26 25 24 2³ 2048 1024 512 256 128 64 32 16 8 2² ~ 4 2¹ 2⁰ 21 22 23 24 2.5 2-6 2 1 0.5 0.25 0.125 0.0625 0.03125 0.015625 N

Systems Architecture

7th Edition

ISBN:9781305080195

Author:Stephen D. Burd

Publisher:Stephen D. Burd

Chapter3: Data Representation

Section: Chapter Questions

Problem 5PE

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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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