Express −7 in 16-bit two’s complement (signed) binary form.

Introduction / Context:Two’s complement is the dominant representation for signed integers in computer systems because it yields a single representation for zero, simplifies arithmetic, and keeps addition/subtraction hardware uniform. This question asks for −7 in 16-bit two’s complement.

Given Data / Assumptions:

• Word size: 16 bits.
• Target value: −7.
• Representation system: two’s complement.

Concept / Approach:

• To obtain −N in two’s complement: write +N in binary, invert all bits (one’s complement), then add 1.
• Ensure the width (16 bits) is maintained throughout.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 0000 0000 0000 0111: That is +7, not −7.
• 1000 0000 0000 0111: Sign-magnitude-like form, not valid two’s complement for −7.
• 1111 0000 0000 0001 and 0111 0000 0000 0000: Do not correspond to two’s complement of 7.
• None of the above: Correct here only because the accurate two’s complement (1111 1111 1111 1001) is not listed among the options.

Common Pitfalls:

• Forgetting to fix the bit-width before inversion and addition.
• Confusing sign-magnitude or one’s complement with two’s complement.

Final Answer: