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CUET PG 2024 Computer PYQ — The range of integers that can be represented by a 2’s comp… | Mathem Solvex | Mathem Solvex

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CUET PG
Computer
Q. 946

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CUET PG 2024 — Computer PYQ

CUET PG | Computer | 2024

The range of integers that can be represented by a 2’s complement number system is _____. Where is n is number of bits in number

Choose the correct answer:

A.
–2^n–1 to 2^n–1 -1
(Correct Answer)
B.
–(2^n–1 –1) to (2^n–1–1)
C.
2^n–1 to 2^n–1
D.
–(2^n–1 + 1) to (2^n–1 – 1)

Correct Answer:

–2^n–1 to 2^n–1 -1

Explanation

Equation Solution

Range nikalne ke liye hum niche di gayi equation ka upyog karte hain:

\text{Lower Limit} = -2^{n-1}

\text{Upper Limit} = 2^{n-1} - 1

Isliye, poori range hogi:

\mathbf{\text{Range} = [ -2^{n-1} \text{ to } 2^{n-1} - 1 ]}

Example (For $n = 8$ bits):

\text{Range} = -2^{8-1} \text{ to } 2^{8-1} - 1

\text{Range} = -2^7 \text{ to } 2^7 - 1

\text{Range} = -128 \text{ to } 127

Answer: 2's complement system ki range $-2^{n-1}$ to $2^{n-1} - 1$ hoti hai.

Explanation

Equation Solution

Range nikalne ke liye hum niche di gayi equation ka upyog karte hain:

\text{Lower Limit} = -2^{n-1}

\text{Upper Limit} = 2^{n-1} - 1

Isliye, poori range hogi:

\mathbf{\text{Range} = [ -2^{n-1} \text{ to } 2^{n-1} - 1 ]}

Example (For $n = 8$ bits):

\text{Range} = -2^{8-1} \text{ to } 2^{8-1} - 1

\text{Range} = -2^7 \text{ to } 2^7 - 1

\text{Range} = -128 \text{ to } 127

Answer: 2's complement system ki range $-2^{n-1}$ to $2^{n-1} - 1$ hoti hai.

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