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Engineering and Tech / Introduction to Engineering Experimentation 3 / Chapter 4 / Problem 4.12

Introduction to Engineering Experimentation | 3rd Edition | ISBN: 9780131742765 | Authors: Anthony J. Wheeler, Ahmad R. Ganji

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How many bits are required for a digital device to

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QUESTION:

How many bits are required for a digital device to represent the decimal number 12,034 in simple binary? How many bits for 2's-complement binary?

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QUESTION:

How many bits are required for a digital device to represent the decimal number 12,034 in simple binary? How many bits for 2's-complement binary?

ANSWER:

Step 1 of 2

The given decima1l number is 12,034.

To convert the decimal number into binary bits, follow the below procedure,

12034
	6017	0
	3008	1
	1504	0
	752	0
	376	0
	188	0
	94	0
	47	0
	23	1
	11	1
	5	1
	2	1
	1	0
	0	1

In the second row, the number 12034 is divided by 2, the quotient will be 6017, and remainder 0.

Similarly, 6017 is divided by 2, the quotient will be 3008 and remainder 1.

In this way, the binary numbers in 0 and 1 are obtained.

Counting from downward direction, the binary conversion of decimal number 12034 is 10111100000010.

Therefore, to represent the decimal number 12034, the number of bits required are 14.

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