Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Let A = 1111 1010 and B = 0000 1010 be two 8-...
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Let A = 1111 1010 and B = 0000 1010 be two 8-bit 2’s complement numbers. Their product in 2’s complement is
- a)1100 0100
- b)1001 1100
- c)1010 0101
- d)1101 0101
Correct answer is option 'A'. Can you explain this answer?
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Let A = 1111 1010 and B = 0000 1010 be two 8-bit 2’s complement ...
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Let A = 1111 1010 and B = 0000 1010 be two 8-bit 2’s complement ...
Explanation:
To find the product of two 2s complement numbers, we can simply multiply them as unsigned binary numbers and then take the 2s complement of the result if the signs of the two numbers being multiplied are different.
A = 1111 1010 (−6 in decimal)
B = 0000 1010 (10 in decimal)
Multiplying these two numbers as unsigned binary numbers gives:
1 1 1 1 1 0 1 0 (A)
× 0 0 0 0 1 0 1 0 (B)
------------------
0 0 0 0 0 0 0 0 (0)
1 1 1 1 1 0 1 0 (A)
------------------
1 0 0 1 1 0 0 0 (−60 in decimal)
Since A and B have different signs, we need to take the 2s complement of the result. The 2s complement of −60 is:
0 1 1 0 1 1 0 0 (60 in binary)
+ 1 (add 1)
------------------
0 1 1 0 1 1 0 1 (−60 in 2s complement)
Therefore, the product of A and B in 2s complement is:
1 1 0 0 0 1 0 0 (−60 in 2s complement)
Answer: Option A (1100 0100)
To find the product of two 2s complement numbers, we can simply multiply them as unsigned binary numbers and then take the 2s complement of the result if the signs of the two numbers being multiplied are different.
A = 1111 1010 (−6 in decimal)
B = 0000 1010 (10 in decimal)
Multiplying these two numbers as unsigned binary numbers gives:
1 1 1 1 1 0 1 0 (A)
× 0 0 0 0 1 0 1 0 (B)
------------------
0 0 0 0 0 0 0 0 (0)
1 1 1 1 1 0 1 0 (A)
------------------
1 0 0 1 1 0 0 0 (−60 in decimal)
Since A and B have different signs, we need to take the 2s complement of the result. The 2s complement of −60 is:
0 1 1 0 1 1 0 0 (60 in binary)
+ 1 (add 1)
------------------
0 1 1 0 1 1 0 1 (−60 in 2s complement)
Therefore, the product of A and B in 2s complement is:
1 1 0 0 0 1 0 0 (−60 in 2s complement)
Answer: Option A (1100 0100)
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Let A = 1111 1010 and B = 0000 1010 be two 8-bit 2’s complement numbers. Their product in 2’s complement isa)1100 0100b)1001 1100c)1010 0101d)1101 0101Correct answer is option 'A'. Can you explain this answer?
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