Which one of the following is decimal equivalent of -bit two's complement number ?

Explanation: The correct option is 1. -45 . Explanation: The given -bit binary number is: In signed number representation using two's complement , the Most Significant Bit (MSB), which is the leftmost bit, acts as the sign bit: If , the number is positive , and its value is calculated directly from its binary form. If , the number is negative . To find its decimal magnitude, we must find its two's complement configuration. Since the leftmost bit here is , the number is negative . Method 1: Using the Weight of the MSB In an -bit signed representation, the positional weights of the bits are given as: Now, map the given binary string onto these weights: Bit Position 7 (MSB) 6 5 4 3 2 1 0 (LSB) Weight Value Given Bit Multiply each bit by its corresponding weight and sum them up:

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NIMCET 2026 — Computer PYQ

NIMCET | Computer | 2026

Which one of the following is decimal equivalent of $8$ -bit two's complement number $11010011$ ?

Choose the correct answer:

Explanation

The correct option is 1. -45.

Explanation:

The given $8$ -bit binary number is:

$Binary Number = 11010011$

In signed number representation using two's complement, the Most Significant Bit (MSB), which is the leftmost bit, acts as the sign bit:

If $MSB = 0$ , the number is positive, and its value is calculated directly from its binary form.
If $MSB = 1$ , the number is negative. To find its decimal magnitude, we must find its two's complement configuration.

Since the leftmost bit here is $1$ , the number is negative.

Method 1: Using the Weight of the MSB

In an $8$ -bit signed representation, the positional weights of the bits are given as:

$- 2^{7}, 2^{6}, 2^{5}, 2^{4}, 2^{3}, 2^{2}, 2^{1}, 2^{0}$

Now, map the given binary string $11010011$ onto these weights:

Bit Position	7 (MSB)	6	5	4	3	2	1	0 (LSB)
Weight	$- 2^{7}$	$2^{6}$	$2^{5}$	$2^{4}$	$2^{3}$	$2^{2}$	$2^{1}$	$2^{0}$
Value	$- 128$	$64$	$32$	$16$	$8$	$4$	$2$	$1$
Given Bit	$1$	$1$	$0$	$1$	$0$	$0$	$1$	$1$

Multiply each bit by its corresponding weight and sum them up:

$Decimal Value = (1 \times - 128) + (1 \times 64) + (0 \times 32) + (1 \times 16) + (0 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1)$

$Decimal Value = - 128 + 64 + 0 + 16 + 0 + 0 + 2 + 1$

$Decimal Value = - 128 + 83$

$Decimal Value = - 45$