26 - Floating Point Number Normalisation

 1. The objectives of normalisation include:

  Unambiguous representation (clear and precise without any confusion)

  to maximise precision

  All of the above

  to simplify arithmetic

 2. The idea behind normalisation (put simply) is that the leading digits of the _________________________ and the exponent increased instead wherever possible.

  mantissa are removed where possible

  exponent are removed where possible

  CPU register are added to, if possible

  binary byte are removed where possible

 3. For positive numbers, the normalised form starts with a ___________________

  1 followed immediately by a zero

  zero followed immediately by a 1

  1 followed by a point and two leading zeros

  zero followed by two 1s

 4. For negative numbers, the normalised form starts with a 1 followed immediately by a zero.



 5. The goal of normalisation, put simply, is to get the binary point in the right position and adjust the_________ accordingly.

  mantissa's zero

  radix or point


  None of the above

 6. This floating point number is stored using 4 bits for both the mantissa and exponent (both two’s complement). You can see straight away that this is not normalised because it ____

  does not end with a zero

  does not start with a 1

  ends with a 1

  starts with three zeros

 7. Typically, the binary point is positioned immediately to the right of the sign bit.



 8. Normalise this floating point number that has 4 bits (in two’s complement) for the mantissa and the same for the exponent.





 9. The floating point number 11000001 is stored using 4 bits for the mantissa and 4 bits for the exponent, both in two's complement. Normalising it would result in:

  Answer: 1000001

  Answer: 01111111

  Answer: 1100000

  Answer: 10000000

 10. The floating point binary number 11101011 is stored using 5 bits for the mantissa and 3 bits for the exponent, both in two's complement. Normalising it would give:

  Answer: 10100001

  Answer: 11100001

  Answer: 00100001

  Answer: 1010111

 11. To normalise positive two's complement numbers, all the leading zeros should be removed with the exception of a single zero.



 12. To normalise negative two's complement numbers, the leading zeros, instead of the leading ones, should be removed (identical to the process for + numbers)



 13. For a two’s complement representation, the truncation error is always positive.



 14. Konrad Zuse was the architect of the Z3 computer, which used a 22-bit binary floating-point representation.



 15. The binary point between the digits b0 and b1 does not exist physically in the computer.
Note: …..or to put it simply, the logic circuits of the computer are designed such that the computations result in numbers that correspond to the assumed location of this point.