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How many bits are required for a digital device to
Chapter , Problem 4.11(choose chapter or problem)
How many bits are required for a digital device to represent the decimal number 27,541 in simple binary? How many bits for 2's-complement binary?
Questions & Answers
QUESTION:
How many bits are required for a digital device to represent the decimal number 27,541 in simple binary? How many bits for 2's-complement binary?
ANSWER:Step 1 of 2
The given decima1l number is 27,541.
To convert the decimal number into binary bits, follow the below procedure,
27541 |
||
13770 |
1 |
|
6885 |
0 |
|
3442 |
1 |
|
1721 |
0 |
|
860 |
1 |
|
430 |
0 |
|
215 |
0 |
|
107 |
1 |
|
53 |
1 |
|
26 |
1 |
|
13 |
0 |
|
6 |
1 |
|
3 |
0 |
|
1 |
0 |
|
0 |
1 |
In the second row, the number 27541 is divided by 2, the quotient will be 13770, and remainder 1.
Similarly, 13770 is divided by2, the quotient will be 6885 and remainder 0.
In this way, the binary numbers 0 and 1 is obtained.
Counting from downward direction, the binary conversion of decimal number 27541 is 100101110010101.
Therefore, to represent the decimal number 27541, the number of bits required are 15.