Perform Restoring division of a) 10110 with 11

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23-06-2024
Computer Science

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Perform Restoring division of a) 10110 with 11

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aryan827373828 aryan827373828 · Answer 1 · 2024-06-23T00:19:54+05:30

Answer:

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Perform Restoring division of a) 10110 with 11

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To perform restoring division of

10110

10110 by

11

11, we proceed through the following steps:

Step-by-Step Restoring Division

Initial Setup:

Dividend:

10110

Divisor:

11

Identify Binary Representation:

10110

10110 is the binary representation of the decimal number

22

22.

Align the Dividend and Divisor:

Align the most significant bits of the divisor with the most significant bits of the dividend.

Divisor

11

11 in binary is

1011

1011.

yaml

Copy code

Dividend: 10110

Divisor: 1011

Initialize the Restoring Division Process:

Compare the divisor with the initial segment of the dividend of the same length.

10110

10110 (dividend) starts with

1011

1011 (divisor).

Subtraction:

Subtract the divisor from the current position of the dividend.

10110

10110 -

1011

1011 =

0011

yaml

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Dividend: 00110

Divisor: 1011

Check MSB (Most Significant Bit):

Check if the result of the subtraction (partial remainder) is non-negative.

0011

0011 (partial remainder) is positive.

Restoring the Dividend:

Since the result was positive, we restore the previous dividend and append

1

1 to the quotient.

00110

00110 becomes

10110

10110.

yaml

Copy code

Dividend: 10110

Divisor: 1011

Quotient: 1

Shift Left:

Shift the current dividend and the quotient to the left by one bit.

New dividend:

0110

0110, Quotient:

10

10.

yaml

Copy code

Dividend: 0110

Divisor: 1011

Quotient: 10

Next Iteration:

Compare

0110

0110 with

1011

1011.

Subtraction:

0110

0110 -

1011

1011 =

1101

1101.

yaml

Copy code

Dividend: 110

Divisor: 1011

Quotient: 101

Check MSB:

1101

1101 is negative, so restore the previous dividend (

0110

0110).

yaml

Copy code

Dividend: 0110

Divisor: 1011

Quotient: 101

Final Steps:

Shift left again.

yaml

Copy code

Dividend: 1100

Divisor: 1011

Quotient: 1011

Subtraction:

1100

1100 -

1011

1011 =

001

001.

yaml

Copy code

Dividend: 001

Divisor: 1011

Quotient: 1011

Check MSB:

001

001 is positive.

Final Restoring and Quotient:

Restore the previous dividend (

1100

1100).

yaml

Copy code

Dividend: 1100

Divisor: 1011

Quotient: 10110

Conclusion

The quotient is

10110

10110 and the remainder is

0

0.

Therefore,

10110

10110 divided by

11

11 in binary form results in a quotient of

10110

10110 and a remainder of

0

0.