Two’s-complement interpretation – does the 8-bit pattern 10011100 represent −100 in decimal?

Introduction / Context: Two’s-complement representation encodes negative values by inverting bits of the magnitude and adding 1. Recognizing a negative 8-bit pattern and recovering its decimal value is a core skill in digital arithmetic and systems programming.

Given Data / Assumptions:

• 8-bit value: 10011100.
• Two’s-complement encoding assumed.
• We must determine its decimal value.

Concept / Approach: For an 8-bit number with MSB 1, the value is negative. To find the magnitude, take two’s complement: invert all bits then add 1. The resulting magnitude is interpreted in ordinary binary and the sign is negative.

Step-by-Step Solution:

Verification / Alternative check: Add the number to its magnitude in two’s complement: 10011100 + 01100100 = 1 00000000 (ignoring the final carry) which is a property confirming correct inversion and addition pairing.

Why Other Options Are Wrong: Ignoring the MSB or using sign-magnitude rules would misinterpret the encoding. Overflow flags are unrelated to static value interpretation.

Common Pitfalls: Forgetting to add 1 after inversion, or miscounting bit weights when converting back to decimal.

Final Answer: Correct