CUET PG 2021 — Computer PYQ

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Question

CUET PG 2021 — Computer PYQ

CUET PG | Computer | 2021

The smallest integer than can be represented by an 8-bit number in 2’s complement form is

Choose the correct answer:

Explanation

Solution

2's complement representation mein, agar humare paas $n$ bits hain, toh integers ki range niche diye gaye formula se nikali jati hai:

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

Yahan, bits ki sankhya $n = 8$ di gayi hai.

1. Smallest Integer (Minimum Value) nikalna:

Formula ke anusar, smallest integer hoga:

\text{Smallest Integer} = -2^{8-1}

\text{Smallest Integer} = -2^7

\text{Smallest Integer} = -128

2. Largest Integer (Maximum Value) nikalna (Extra Info):

\text{Largest Integer} = 2^{8-1} - 1

\text{Largest Integer} = 2^7 - 1

\text{Largest Integer} = 128 - 1 = 127

Binary Representation:

$-128$ ko 8-bit 2's complement mein aise likha jata hai:

10000000_2

Answer:

Smallest integer jo 8-bit 2’s complement form mein represent ho sakta hai, wo hai $-128$ .