Question

The decimal equivalent 8-bit two's complement number \(11010011\):

• A. \(-211\)
• B. \(-45\)
• C. \(-44\)
• D. \(+211\)

Hint:

For a negative two's complement number: Invert bits → Add 1 → Convert to decimal → Attach negative sign.

Answer 1

The Correct Option is B

Step 1: Read the sign bit.
The number is $11010011$. Its most significant bit is $1$, so in 8-bit two's complement this value is negative.
Step 2: Plan the magnitude recovery.
To find how negative it is, take the two's complement (invert all bits and add one) to recover the positive magnitude.
Step 3: Invert every bit.
$11010011$ flipped becomes $00101100$.
Step 4: Add one.
$00101100 + 1 = 00101101$.
Step 5: Convert the magnitude to decimal.
$00101101 = 32 + 8 + 4 + 1 = 45$.
Step 6: Restore the sign.
Because the original sign bit was $1$, the value is $-45$.
\[ \boxed{-45} \]