Radix Complement Arithmetic (1)

• Radix complement number systems are used to convert subtraction to addition, which reduces hardware requirements (only adders are needed).

• A - B = A + (-B) (add r’s complement of B to A)

• Range of numbers in two’s complement number system:

, where n is the number of bits.

• 2n-1 -1 = (0, 11 ... 1)2cns and -2n-1 = (1, 00 ... 0)2cns

• If the result of an operation falls outside the range, an overflow condition is said to occur and the result is not valid.

• Consider three cases:

  • A = B + C,
  • A = B - C,
  • A = - B - C,
    (where B ³ 0 and C ³ 0.)
    

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