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28 - Floating Point Arithmetic (Add/Subtract)

 1. While performing floating point binary addition or subtraction, the following steps are uesful to have as a guideline to follow. Fill in the blanks.
1. Make sure both numbers are 1._______________
2. Make the 2.____________ the same
3. If performing subtraction, 3.________ the number to subtract
4. Add 4.___________ together
5. Normalise the result if necessary.

  1. Normalised 2. Exponents 3. Negate 4. Mantissa's

  1. both in floating point binary form. 2. Mantissa's 3. invert the bits and add one 4. Exponents

  1. Exponents 2. Mantissa's 3. Negate 4. Exponents

  None of the above

 2. In the example below, what is happening at point 1 and 2?
kevindrummexample.png

  None of the above

  1. Add the mantissa's to the exponents 2. Add the exponents

  1. Add the expnents together 2. Add the mantissa's together

  1. Making the exponents the same 2. Add the mantissa's together

 3. Fill in the blanks for point 1. and the final result in the following image.
floatingpoint_add.png

  Answer: 0.1111101 x 2 to th e power of 3. Final Answer: 01111111 0111

  None of the above

  It is not possible to perform this floating point binary addition.

  Answer: 0.0000010 x 2 to the power of 4. Final Answer: 01010110 0100

 4. In the question and worked answer below, can you explain what is happening in the blank?
floatingpoint_add1.png

  Addition of the mantissa's

  Making the exponent's the same before adding them

  A truncation error

  An overflow + flag and underflow error all at once

 5. In the following worked question and answer, can you fill in the blanks for what is happening in '1' and suggest what should happen next?
floatingpoint_subtract.png

  None of the above

  1. Invert all the bits and add one. What should happen next? Nothing - the answer is as it should be.

  1. Negate the number to subtract. What should happen next? The result should be normalised

  1. Negate the number to subtract. What should happen next? The exponents should be made the same again.