ISRO CS 2025 Q.51: solution and answer

ISRO 2025 · CSQ.51 · 1 mark · MCQ

Let A = (11111010)_2 and B = (00001010)_2 represent numbers in 2's complement and stored as 1 byte. The product of A and B in 2's complement is

(A)
(1001 1100)_2
(B)
(1010 0101)_2
(C)
(1100 0100)_2
(D)
(1101 0101)_2

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Answer and solution

ANSWER

The product is $- 60$ , stored in 8-bit 2's complement as $(11000100)_{2}$ , option (c).

Official answer: CSource: ISRO's final answer key of 15 May 2026

The sign bit of $A = (11111010)_{2}$ is 1, so $A$ is negative. Invert the bits to get $00000101$ and add 1 to get $00000110 = 6$ . So $A = - 6$ .
$B = (00001010)_{2}$ has sign bit 0, so $B = + 10$ .
The product is $(- 6) \times 10 = - 60$ . This lies in the 8-bit 2's complement range $[- 128, 127]$ , so there is no overflow.
The 8-bit 2's complement representation of $- 60$ is $2^{8} - 60 = 196$ .
To check by bits, write $60 = 00111100$ . Invert to $11000011$ and add 1 to get $11000100$ . Also $196 = 128 + 64 + 4$ , which gives $11000100$ .
So the product is $(11000100)_{2}$ , which is option (c).
The other options read $156$ , $165$ and $213$ as unsigned numbers. As signed 8-bit values they are $- 100$ , $- 91$ and $- 43$ . None of these is $- 60$ .

KEY IDEA

Decode each 2's complement number to its signed value, multiply as ordinary integers, check the result fits in 8 bits, then encode it back as $2^{8}$ plus the negative value.

WATCH OUT FOR

Reading $11111010$ as the unsigned number 250, or forgetting to add 1 after inverting the bits. Either gives a wrong magnitude for $A$ and a wrong product.

From the ISRO CS 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 2 ISRO Number systems questions, with notes