# 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.

TRUE

FALSE

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

mantissa's zero

exponent

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

ends with a 1

starts with three zeros

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

TRUE

FALSE

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:

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:

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

FALSE

TRUE

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)

TRUE

FALSE

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

TRUE

FALSE

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

TRUE

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.`

TRUE

FALSE