Exam-style question
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Using 6-bit two’s complement, represent -18 and state the range of values available with 6 bits. Show the conversion steps.
Model answer
What a good answer should say
- The positive value 18 is 010010 in 6 bits.
- Invert the bits to obtain 101101, then add 1 to obtain 101110.
- Therefore, -18 is represented as 101110.
- The 6-bit range is -32 to 31.
Explanation
Why this works
A negative two’s complement value is formed by writing the positive magnitude in the specified number of bits, inverting every bit, and adding 1. The range is calculated as -2^(6-1) to 2^(6-1)-1, which is -32 to 31.
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