Floating Point Subtraction
Computer Science: OCR A Level, topic 4.1.17
Floating Point Subtraction
When subtracting floating point binary numbers, it is important to ensure each number is represented with the same level of precision. This means that the exponents must be the same.
Subtraction
- The example below shows the subtraction of two normalised 12-bit floating point numbers, with 8-bit mantissas and 4-bit exponents:
- 0.10110000011 − 0.11100000010
Matching exponents
- The first step is to ensure the exponents of the two numbers match, by adding 1 to the exponent of the second number (2) to match that of the first (3).
- Adding 1 to the exponent of the second number moves the binary point of the mantissa in this number one place to the left:
- 0.11100000010 0.01110000011
Two's complement
- The next step is to find the twos complement of the second number:
- 1.1001000
Add mantissas
- The two mantissas can then be added:
- 0.1011000 + 1.1001000 = 0.1000000
- Note that the first digit of the two's complement corresponds to -1 in decimal.
- Factor this in when you do the addition.
Normalise the result
- The result should then be normalised by moving the binary point one place to the left.
- That means we add 1 to the exponent:
- 1.00100000100
Test yourself on Floating Point Subtraction
What are the steps of subtracting floating points?