Negative Binary Numbers
Computer Science: Cambridge International GCSE, topic 1.1.2
Negative Binary Numbers
There exist two systems to express negative numbers in binary.
Sign and magnitude
- The most significant bit of the binary number is a designated sign bit.
- If the number is positive then the MSB is set to 0.
- If the number is negative then the MSB is set to 1.
Sign and magnitude
- This method allows us to express negative numbers.
- However, it is very hard to perform arithmetic using this representation.
Two's compliment
- The place value of the MSB is made negative.
- This allows us to express negative numbers by subtracting the largest possible place value, and then adding the difference back on.
Two's compliment
- This method is much easier to perform calculations with since we can express subtraction as follows:
- a - b = a + (-b)
- This means we do not need a separate subtractor circuit in our processor.
Test yourself on Negative Binary Numbers
Which representation is easier to perform maths with?
Which of the following statements about negative binary numbers are true?