Suppose that 16-bit two's complement numbers are being employed. Consider the bit pattern:

1111 1111 1110 0100

What decimal integer most likely corresponds to these sixteen bits:

Question

Suppose that 16-bit two's complement numbers are being employed. Consider the bit pattern:

1111 1111 1110 0100

What decimal integer most likely corresponds to these sixteen bits:

BlackTom AI · Accepted Answer

We’re working with 16-bit two’s complement representation. The given bit pattern is 1111 1111 1110 0100.

First, recognize that the most significant bit is 1, which means this value is negative in two’s complement.

To find the magnitude, compute the two’s complement (invert all bits and add 1). Inverting 1111 1111 1110 0100 gives 0000 0000 0001 1011. Adding 1 yields 0000 0000 0001 1100, which is 28 in decimal.

Since the original pattern was negative (MSB = 1), the decimal value is −28.

Now evaluate each answer choice:
- +65508: This is a large positive number and does not match a negative, two’s complement 16-bit value. It would correspond to a pattern starting with 0, not 1.
- −29: This is close but incorrect. The two’s complement magnitude we found is 28, not 29, so this would require a different bit pattern.
- −28: This matches our calculation exactly. The pattern 1111 1111 1110 0100 represents −28 in 16-bit two’s complement.
- −32740: This would correspond to a much larger magnitude negative value, inconsistent with the given bit pattern.
- +65507: Like +65508, this is a large positive number and cannot correspond to a negative two’s complement 16-bit pattern.

In summary, the bit pattern 1111 1111 1110 0100 encodes −28 in 16-bit two’s complement, and the other options fail due to sign or magnitude mismatches.

COMP10002_2025_SM2 Supplementary or Special Exam: Foundations of Algorithms (COMP10002_2025_SM2)- Requires Respondus LockDown Browser

Suppose that 16-bit two's complement numbers are being employed. Consider the bit pattern: 1111 1111 1110 0100 What decimal integer most likely corresponds to these sixteen bits:

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