6. Convert -32.296875 to the floating-point binary representation (14-bit model used during the class).

Answered: 6. Convert -32.296875 to the…

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

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6. Convert -32.296875 to the floating-point binary representation (14-bit model used during the class).

Expert Solution

Step 1

To convert -32.296875 into floating point binary representation, first convert it into binary.
For this, divide the number by 2 and get the integer quotient for the next iteration. Record the remainder for the binary digit. Repeat the steps until the quotient is equal to 0.

	quotient	remainder
2	32	0
2	16	0
2	8	0
2	4	0
2	2	0
2	1	1
	0

32 = (100000)₂

To convert the fraction part into binary, In the fraction multiply by 2 and record the resulting integer and fractional part. Continue multiplying by 2 until fractional part equal to zero.

0.296875 x 2	0.593740	0
0.593740 x 2	1.187480	1
0.187480 x 2	0.374960	0
0.374960 x 2	0.749920	0
0.749920 x 2	1.499840	1
.499840 x 2	0.999680	0
0.999680 x 2	1.999360	1
0.999360 x 2	1.998720	1

Hence, 0.296875=(0.01001011)₂

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