Which of the following decimal numbers is equal to 1111 1111 1111 10012SC (16 bit two’s complement representation)

Question

BlackTom AI · Accepted Answer

Let's parse the given 16-bit two's complement binary number: 1111 1111 1111 1001_2.

Option 1: -7. To verify, compute the two's complement magnitude. Invert all bits: 0000 0000 0000 0110. Add 1: 0000 0000 0000 0111, which is 7 in unsigned form. Since the original MSB was 1, the value is negative, so the decimal value is -7. This matches the option.

Option 2: -6. If the value were -6, the two's complement representation would correspond to the magnitude of 6 after inverting and adding 1. Invert 1111 1111 1111 1001 to get 0000 0000 0000 0110; adding 1 yields 0000 0000 0000 0111 (7). That would represent -7, not -6, so this option is incorrect.

Option 3: 6. A positive 6 would require the MSB to be 0 in two's complement. Since the given number starts with 1, it cannot be +6. This option is therefore incorrect.

Option 4: -9. The two's complement magnitude process would have to give 9 after inversion and +1. Inverting 1111 1111 1111 1001 yields 0000 0000 0000 0110, add 1 gives 0000 0000 0000 0111 (7). It does not yield 9, so -9 is incorrect.

Option 5: None of the options. Since we have verified that -7 is the correct interpretation, this option is not true.

CSE-12-02 Quiz 4 : Number Conversions

Which of the following decimal numbers is equal to 1111 1111 1111 10012SC (16 bit two’s complement representation)

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