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Construct an example to show that three guard bits are needed to produce the correct answer...

Construct an example to show that three guard bits are needed to produce the correct
answer when two positive numbers are subtracted.

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ANSWER:-

To construct an example to show that three guard bits are needed to produce the correct answer when two positive numbers are subtracted:-

  • Let consider A and B are 6-bit i.e. normalized mantissas of floating point numbers.
  • Because of differences in exponents, B must be shifted 6 positions before subtraction.
  • Let take A = 0.100000 and B = 0.100001
  • After shifting, we get,

A = 0.100000 000 and B = 0.000000 101 ← Three Guard bit

  • Now perform subtraction, i.e., A - B = 0.011111 011 (binary subtraction is performed)
  • Hence, Normalize Value = 0.111110 110
  • Therefore, Rounded Value = round 0.111111 (correct answer)
  • But with 2 Guard bits we would have

A = 0.100000 00 and B = 0.000000 11

  • Perform Subtraction operation, i.e., A - B = 0.011111 01
  • Hence, Normalized Value = 0.111110 10
  • Therefore, Rounded Value = 0.111110. The value is not efficient as above.
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