Question:
What is the 8-bit 2's complement representation of the decimal number -77?
What is the 8-bit 2's complement representation of the decimal number -77?
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Write 77 as 01001101, invert the bits, then add 1.
Updated On: Jul 2, 2026
- 10110011
- 01001101
- 10110011
- 11001100
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The Correct Option is A
Solution and Explanation
Step 1: Start with the magnitude \(77\) as an 8-bit binary number: \(64+8+4+1 = 77\), so \(77 = 01001101\).
Step 2: To form the 2's complement (the representation of the negative value), first invert every bit of 01001101. This gives the 1's complement 10110010.
Step 3: Add 1 to the 1's complement: \[10110010 + 1 = 10110011\]
Step 4: So \(-77 = 10110011\). The MSB is 1, confirming a negative value. This matches option (A). Note that option (B), 01001101, is simply \(+77\), and options (A) and (C) print the same correct pattern.
Step 2: To form the 2's complement (the representation of the negative value), first invert every bit of 01001101. This gives the 1's complement 10110010.
Step 3: Add 1 to the 1's complement: \[10110010 + 1 = 10110011\]
Step 4: So \(-77 = 10110011\). The MSB is 1, confirming a negative value. This matches option (A). Note that option (B), 01001101, is simply \(+77\), and options (A) and (C) print the same correct pattern.
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