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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.

  None of the above

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

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

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

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

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

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

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

  None of the above

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

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

  None of the above

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

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

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

  Making the exponent's the same before adding them

  An overflow + flag and underflow error all at once

  Addition of the mantissa's

  A truncation error

 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

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

  None of the above

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

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


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