Convert the binary number below into floating-point representation - Scottish Highers Computing Science - Question 3 - 2023
Question 3
Convert the binary number below into floating-point representation.
–0.0000 0101 0000 1111
There are 16 bits for the mantissa (including the sign bit) and 8 bits f... show full transcript
Worked Solution & Example Answer:Convert the binary number below into floating-point representation - Scottish Highers Computing Science - Question 3 - 2023
Step 1
Sign
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Answer
The sign bit is determined by the first bit of the binary number. Here, it is 1 since the number is negative.
Step 2
Remaining mantissa
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Answer
The remaining mantissa consists of the next 15 bits after the sign bit. Thus, we take the bits 10100001111000.
Step 3
Exponent
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Answer
The exponent is given by the last 8 bits of the binary number, which is 11101101.
Step 4
Effect of increasing the number of bits allocated to the mantissa
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Answer
Floating point numbers could be stored more precisely/accurately.
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