3.1.2

Negative Binary Numbers

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Negative Binary Numbers

There exist two systems to express negative numbers in binary.

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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.
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Sign and magnitude

  • This method allows us to express negative numbers.
  • However, it is very hard to perform arithmetic using this representation.
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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.
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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.

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1Problem Solving

2Programming

3Data

4Computers

5Communication & The Internet

6The Bigger Picture

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