ITPEC IP October 2025 Question 2
Which of the following is the binary number that is obtained by adding the binary numbers 01011010 and 01101011? Here, the binary numbers are expressed as positive 8-bit values.
Explanation
11000101 — add the two 8-bit values column by column from the right, carrying 1 whenever a column reaches 2.
In decimal, 01011010 is 64 + 16 + 8 + 2 = 90 and 01101011 is 64 + 32 + 8 + 2 + 1 = 107, so the sum is 90 + 107 = 197.
In binary, from the right: bit 0 is 1; bit 1 is 0 carry 1; bit 2 takes the carry to give 1; bits 3, 4 and 5 each give 0 carry 1; bit 6 is 1 + 1 + 1, so 1 carry 1; bit 7 takes the last carry to give 1. The result is 11000101, which is 128 + 64 + 4 + 1 = 197.
Answer (d)
Why not others:
- •(a) 00110001 — this is the bitwise XOR of the two values: each column added with every carry thrown away (49)
- •(b) 01111011 — this is the bitwise OR, setting a 1 wherever either value has one; it ignores that 1 + 1 is 0 carry 1 (123)
- •(c) 10000100 — equals 132, not 197; it is the bit-by-bit inverse of the OR in (b), not a sum
Key rule: Binary addition is not a bitwise operation: 1 + 1 = 102, so write 0 and carry 1 to the next column; check the result by converting to decimal.
Basic Theory · AI-written, may contain errors
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