Fractional Numbers

Question 1

Define Fixed Point Form

Answer 1

• Represents Fractional numbers

- Binary point is set in fixed position, does not need to be stored in memory

Question 2

How to convert recurring number to fixed point form

Answer 2

• Convert whole part of the number
• Multiply fractional part by 2
• Until fraction part is 0, already converted (repetition) or fraction space is full

Question 3

Range of Unsigned Fixed Point Form numbers

Answer 3

1…1 to 0…01

Question 4

Range of Signed Fixed Point Form numbers

Answer 4

01…1 to 0…01

Question 5

Range of Negative Signed Fixed Point Form Numbers

Answer 5

10…0 to 1…1

Question 6

Large number of bits for the whole part in floating point form results in

Answer 6

allows large values to be represented, but without the detail of the fractional part

Question 7

Large number of bits for the fractional part results in

Answer 7

very small numbers yet increasingly precise values to be represented

Question 8

Floating Point Forms are made from

Answer 8

• Mantissa

- Exponent

Question 9

What to do with positive mantissa and negative exponent

Answer 9

• Find value and move point left by value

- Fill in with 0s

Question 10

What to do with negative mantissa and positive exponent

Answer 10

-move right by value of exponent

Question 11

What to do with negative mantissa and exponent

Answer 11

• Find value and move left by value

- Fill in with 1s

Question 12

Define normalisation (Floating Point)

Answer 12

• Unique representation for a number
• Maximum possible precision
• Either 1.0, 0.1

Question 13

How do you normalise

Answer 13

• One place to right (x2) reduce exponent by 1 (/2)

- One place to the left (/2) increase exponent by 1 (x2)

Question 14

Define Underflow

Answer 14

Calculation result is too small to be represented with available number of bits