normalize floating point

Question

i am doing floating point addition using MARS.

  SameExponent:
  add $s6,$s4,$s5

after I aligned the exponents, I added up the significands,but how do I detect if the sum is still normalized or not in order to shift the signicicand to the left or right? Thank you

Is this the MARS MIPS simulator? If so you might want to tag it with mips as well. — Andy, Apr 24 '11 at 17:29

score 1 · Accepted Answer · edited May 23 '17 at 12:29

If the significands are integers in the range -A ... +A, then the result of adding them together is in the range -2A ... +2A. To normalize the result you need to shift left or right to get the most-significant 1 bit back to the normalized position, keeping track of how much you shifted so you can adjust the exponent accordingly.

The maximum required right shift is one position; the left shift can be more if your arguments may be positive or negative. The simple way to do it is a while-style loop, shifting left by one until the MSB is where you want.

Algorithm for finding the smallest power of two that's greater or equal to a given value has some alternate possibilities if you want something faster (nothing for MIPS though).

normalize floating point

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