CUET PG 2022 — Computer PYQ

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Question

CUET PG 2022 — Computer PYQ

CUET PG | Computer | 2022

Given below are two statements:
Statement I: 011010 is 2’s complement representation of –37.
Statement II: 111(8) is octal representation of 73.
In the light of the above statements, choose the most appropriate answer from the options given below:

Choose the correct answer:

Explanation

Solution for Statement I

Hume check karna hai ki kya $011010$ , $-37$ ka 2's complement hai.

Rule: Agar koi number 2's complement mein $0$ se start hota hai, toh wo hamesha ek positive number hota hai.
Diya gaya binary: $011010$ .
Kyunki MSB (Most Significant Bit) $0$ hai:

$\text{Value} = (1 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (0 \times 2^0)$

$\text{Value} = 16 + 8 + 0 + 2 + 0 = +26$
$-37$ ko represent karne ke liye hume kam se kam $7$ bits chahiye kyunki $2^5 = 32$ , jo 37 se chota hai.
Conclusion: $011010$ ki value $+26$ hai, $-37$ nahi. Isliye Statement I Galat (False) hai.

Solution for Statement II

Hume check karna hai ki kya $111_{8}$ decimal mein $73$ ke barabar hai.

Octal ko Decimal mein badalne ka formula:

$\text{Decimal} = (d_2 \times 8^2) + (d_1 \times 8^1) + (d_0 \times 8^0)$
Values put karte hain ( $111$ ):

$\text{Value} = (1 \times 8^2) + (1 \times 8^1) + (1 \times 8^0)$

$\text{Value} = (1 \times 64) + (1 \times 8) + (1 \times 1)$

$\text{Value} = 64 + 8 + 1 = 73$
Conclusion: Statement II bilkul Sahi (True) hai.

Final Answer

Upar diye gaye calculation ke mutabik:

Statement I is False.
Statement II is True.

Sahi Option: Statement I galat hai lekin Statement II sahi hai.