The decimal number 6.125 converted to binary is 110.001 - Scottish Highers Computing Science - Question 4 - 2019
Question 4
The decimal number 6.125 converted to binary is 110.001.
Convert 110.001 to floating-point representation. There are 16 bits for the mantissa (including the sign bit... show full transcript
Worked Solution & Example Answer:The decimal number 6.125 converted to binary is 110.001 - Scottish Highers Computing Science - Question 4 - 2019
Step 1
Sign bit:
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Answer
The sign bit indicates whether the number is positive or negative. Since 110.001 is a positive number, the sign bit is 0.
Step 2
Remaining 15 bits of mantissa:
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Answer
After the sign bit, the next 15 bits of the mantissa are needed. The binary for 110.001 is 110.001000000000000. By normalizing it to the form 1.xxxxxx, we adjust it:
Normalized form: 1.10001 × 2^2
Thus, the mantissa will be '100010000000000' (the '1' is implicit in floating-point representation).
Step 3
Exponent:
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Answer
The exponent for this floating-point representation will be calculated by adding the bias to the actual exponent. The bias for an 8-bit exponent is 127:
Actual exponent: 2
Exponent with bias: 2 + 127 = 129
In binary, 129 is '10000001'.
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