P2 T1 L7 - Floating point numbers

Question 1

What are real numbers? (in the context of computing)

1 point

Answer 1

1. In the context of Computing, Real Numbers are numbers with a fractional part.

Question 2

Real numbers can be stored in ______ point and ______ point.

Answer 2

fixed

floating

Question 3

Explain fixed point

1 point

Answer 3

1. Fixed Point representation (where the point cannot move), they have a pre-determined number of bits before and after the point

Question 4

Explain floating point

1 point

Answer 4

1. Floating Point (where the point does move), you get more accuracy and a larger range of numbers you can represent

Question 5

Layout of unsigned integer

Answer 5

Integer |

Question 6

Layout of signed integer

Answer 6

sign | integer |

Question 7

Layout of unsigned fixed point

Answer 7

integer | fraction |

Question 8

Layout of signed fixed point

Answer 8

sign | integer | fraction |

Question 9

Layout of floating point

Answer 9

sign | mantissa | sign | exponent |

Question 10

(Fixed point)
Has a specific number of bits (or digits) reserved for the ______ part (the part to the left of the decimal point) and a specific number of bits reserved for the _______ part (the part to the right of the decimal point).

No matter how large or small your number is, it will always use the same number of bits for each portion.

Decimal point stays in the same position

Decimal point is not ______ (Does not take up any bit positions)

Answer 10

integer

fractional

stored

Question 11

__________ is the process of moving the binary point of a floating point number to provide the maximum level of precision for a given number of bits

Answer 11

Normalisation

Question 12

Why do we do normalisation?

3 points

Answer 12

1. To make best use of the available bits
2. To prevent a loss of bits causing a loss of accuracy
3. Typically used to represent very large or very small numbers by storing a mantissa and an exponent in a 16-bit word (i.e. two bytes) or 32 bit.

Question 13

What are the rules of normalisation?

3 rules

Answer 13

1. Only 1 bit before the decimal point
2. DENARY ONLY: the bit before decimal point must be non-zero (e.g. 3.255 * 10^1)
3. BINARY ONLY: the bit before the decimal point is the sign (e.g. 0.1101 * 2^3)

Question 14

What is the exponent?

1 point

Answer 14

1. The exponent is used as a multiplier to move the mantissa to the correct ‘size’

Question 15

Convert the binary floating point number, 01101010, to a decimal, to denary.
(In this example the mantissa has 5 bits and the exponent has 3.)

(5 steps)

Answer 15

1. Mantissa = 01101, Exponent = 010
2. Insert decimal point (always goes between digits 1 and 2 OR between the sign and the mantissa) = 0.1101
3. Exponent is positive (using 2s compliment), denary value = 2
4. Move the decimal point 2 places to the right = 011.01
5. Fixed point number to denary = 3.25