Question:
The decimal equivalent 8-bit two's complement number \(11010011\):
The decimal equivalent 8-bit two's complement number \(11010011\):
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For a negative two's complement number:
Invert bits → Add 1 → Convert to decimal → Attach negative sign.
Updated On: Jun 11, 2026
- \(-211\)
- \(-45\)
- \(-44\)
- \(+211\)
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The Correct Option is B
Solution and Explanation
Concept:
In an 8-bit two's complement system:
• If MSB = 0, the number is positive.
• If MSB = 1, the number is negative.
Given: \[ 11010011 \] MSB is 1, so the number is negative.
Step 1: Take two's complement to find magnitude.
Invert all bits: \[ 11010011 \rightarrow 00101100 \] Add 1: \[ 00101100+1 = 00101101 \]
Step 2: Convert magnitude into decimal.
\[ 00101101 = 32+8+4+1 = 45 \]
Step 3: Apply sign.
Since original number was negative, \[ 11010011_2=-45 \] Therefore \[ \boxed{\text{Answer (B)}} \]
• If MSB = 0, the number is positive.
• If MSB = 1, the number is negative.
Given: \[ 11010011 \] MSB is 1, so the number is negative.
Step 1: Take two's complement to find magnitude.
Invert all bits: \[ 11010011 \rightarrow 00101100 \] Add 1: \[ 00101100+1 = 00101101 \]
Step 2: Convert magnitude into decimal.
\[ 00101101 = 32+8+4+1 = 45 \]
Step 3: Apply sign.
Since original number was negative, \[ 11010011_2=-45 \] Therefore \[ \boxed{\text{Answer (B)}} \]
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