Exam-style question
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Use the following simplified floating-point convention: the 8-bit mantissa has its binary point immediately after the sign bit, and the 8-bit exponent is stored in two's complement. Convert mantissa 11000000 and exponent 00000010 to decimal. Show how the two's-complement mantissa and exponent are interpreted.
Model answer
What a good answer should say
- The value is -2.
Explanation
Why this works
The mantissa 11000000 is negative in two's complement. Interpreted as an 8-bit integer it is -64; with the binary point after the sign bit, it represents -64/128 = -0.5.
The exponent 00000010 represents +2. Therefore, the floating-point value is -0.5 × 2^2 = -2.
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