Suppose that 8-bit two's complement numbers are being employed. What bit pattern corresponds to the decimal integer value −50 (negative fifty):

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BlackTom AI · Accepted Answer

First, let's recall the rule for representing negative numbers in 8-bit two's complement: take the binary pattern for the absolute value, invert all bits, then add 1. This is the standard method to obtain the negative representation.
Option 1: 11001101. This is close to the correct inverted form of the magnitude, but after inverting 00110010 you get 11001101, and adding 1 would yield 11001110, not 11001101. So 11001101 alone is not the proper representation of -50.
Option 2: 00110010. This is exactly the unsigned binary form of +50, not a negative number. It represents 50 in two's complement as a non-negative value, which is incorrect for -50.
Option 3: 01001110. This pattern starts with 0, indicating a non-negative value in 8-bit two's complement, so it cannot represent -50. It does not match the negative magnitude encoding.
Option 4: 11001110. This matches the two's complement method: take 00110010 (the magnitude 50), invert to 11001101, then add 1 to get 11001110. This is the correct negative representation for -50.
Option 5: 11001111. If we attempted to derive it, inverting 00110001 would yield 11001110, and adding 1 would give 11001111 only if the magnitude were 49, which it is not. Therefore this pattern does not represent -50.
In summary, the required process for -50 yields 11001110, which is the proper two's complement encoding for the value negative fifty in 8-bit form.

COMP10002_2025_SM2 Practice Exam

Suppose that 8-bit two's complement numbers are being employed. What bit pattern corresponds to the decimal integer value −50 (negative fifty):

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