Exam-style question
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A fixed-point format uses 8 bits, with 4 bits before the binary point and 4 bits after it. Convert decimal 5.375 into this fixed-point binary representation. Then convert your result back to decimal to verify it.
Model answer
What a good answer should say
- 5.375 is represented as 0101.0110.
Explanation
Why this works
The integer part 5 is 0101. For the fractional part, 0.375 = 1/4 + 1/8, so the fractional bits are 0110: 0/2 + 1/4 + 1/8 + 0/16 = 0.375.
The complete representation is 0101.0110. Converting back gives 5 + 0.25 + 0.125 = 5.375.
Common mistake
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