ITPEC IP April 2022 Question 3
Which of the following is the binary result of the multiplication of binary 1011 and binary 101?
Explanation
110111 — multiply the binary numbers by shifting and adding, and check in decimal: 11 × 5 = 55.
Multiply 1011 by each bit of 101, shifting one place left per bit:
- •bit 1 (value 1):
1011 - •bit 2 (value 0):
0000 - •bit 3 (value 1):
101100 - •sum:
1011+101100=110111
Check: 1011 is 8 + 2 + 1 = 11, 101 is 4 + 1 = 5, and 110111 is 32 + 16 + 4 + 2 + 1 = 55 = 11 × 5.
Answer (d)
Why not others:
- •(a) 1111 — is 15, the bitwise OR of
1011and0101, not their product - •(b) 10000 — is 16, the sum 11 + 5, not the product
- •(c) 101111 — is 47, eight short of 55; bits 3 and 4 are wrong, as when the carry from adding the two partial products goes astray
Key rule: Binary multiplication is shift-and-add: write the multiplicand shifted once for every 1 bit of the multiplier and add the rows; converting to decimal is a quick check.
Basic Theory · AI-written, may contain errors
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