GATE CSE 2002 | Question: 1.16

Question

Sign extension is a step in 

• A. floating point multiplication
• B. signed $16$ bit integer addition
• C. arithmetic left shift
• D. converting a signed integer from one size to another

Comments

Sign extension is a step in converting a signed integer from one size to another. This process ensures that the sign (positive or negative) of the integer remains the same when its size is increased. For instance, if an 8-bit signed integer needs to be converted to a 16-bit signed integer, sign extension replicates the most significant bit (the sign bit) of the 8-bit integer to fill the additional bits in the 16-bit integer. This preserves the numerical value and sign of the original integer in the larger bit representation.

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Is it valid in Sign magnitude system ? @ritiksri8

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The paragraph by @ritiksri8 is correct only for 1's & 2's complement representations, NOT correct for sign-magnitude representation or Unsigned numbers.

Sign Extension in ALL Representations: https://youtu.be/dkoaDtyiz9k

Answer 1

(D) is the answer. Sign extension (filling the upper bits using the sign bit) is needed while increasing the number of bits for representing a number. For positive numbers, $0$ is extended and for negative numbers $1$ is extended.

Comments

Sign extension is also used in arithmetic right shift.

Ref: https://stackoverflow.com/questions/15729765/sign-extension-with-bitwise-shift-operation

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@reena_kandari not only sign along with sign value also has to be maintained which clearly isnt maintaied in right shift.

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Also called padding

Answer 2

It is used if we want to store one register value into another register.

for example if we want to transfer a register value which can store 8 bits into register which can store 16 bits in that case we have

to fill the empty bits in 16 bits register with signed values

Answer 3

Detailed Video Explanation of Sign Extension in ALL Number Representations: https://youtu.be/dkoaDtyiz9k

$\color{red}{\text{Sign Extension in Various Number Representations:}}$

Consider an n-bit binary number: $a_n a_{n-1} \dots a_1.$ If we want to store/copy this number in $n+r$ bits, then in various number representations, it is carried out in different ways, keeping the number same, with same sign & magnitude.

1. Unsigned Representation:

Pad $r$ $0's$ to the left. So, we get: $000 \dots 0a_n a_{n-1} \dots a_1.$

For example: If $r = 3,$ we get: $000a_n a_{n-1} \dots a_1.$

2. Sign Magnitude Representation:

Keep the MSB same as original binary number i.e. $a_n.$

Pad $r$ $0's$ after the MSB, then the magnitude $a_{n-1} \dots a_1.$.

So, we get: $a_n000 \dots 0a_{n-1} \dots a_1.$

For example: If $r = 3,$ we get: $a_n000a_{n-1} \dots a_1.$

3. 1's Complement Representation:

Copy the MSB $a_n,$ $r$ extra times to the left.

So, we get: $a_na_n \dots a_na_na_{n-1} \dots a_1.$

For example: If $r = 3,$ we get: $a_na_na_na_na_{n-1} \dots a_1.$

4. 2's Complement Representation:

Copy the MSB $a_n,$ $r$ extra times to the left.

So, we get: $a_na_n \dots a_na_na_{n-1} \dots a_1.$

For example: If $r = 3,$ we get: $a_na_na_na_na_{n-1} \dots a_1.$

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Detailed Video Explanation of Sign Extension in ALL Number Representations: https://youtu.be/dkoaDtyiz9k

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Related Important Lectures:

Range of Binary Numbers in ALL Representations: https://youtu.be/JxK_KfSa4GY

Comments

Thank you sir, for summary

Answer 4

D it is used to increment the number of bits of a number

Answer 5

https://en.wikipedia.org/wiki/Sign_extension

Answer 6

d