Write the following binary number using floating-point representation - Scottish Highers Computing Science - Question 2 - 2022
Question 2
Write the following binary number using floating-point representation.
-111 0000 1111.0101
There are 16 bits for the mantissa (including the sign bit) and 8 bits f... show full transcript
Worked Solution & Example Answer:Write the following binary number using floating-point representation - Scottish Highers Computing Science - Question 2 - 2022
Step 1
sign bit
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Answer
The sign of the number is negative, hence the sign bit is set to 1.
Step 2
mantissa: 111 0000 1111.0101
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Answer
The mantissa consists of the binary number without the sign, leading to the representation:
111000011110101
This is then adjusted to fit the 16-bit mantissa requirement:
1110000111101010
(padding with an additional zero at the end as needed).
Step 3
exponent: 0000 1011
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Answer
The exponent is derived from the scientific notation of the binary number. The exponent in this case is 11, which in binary is represented as:
00001011
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