Fractional Numbers Flashcards
Define Fixed Point Form
- Represents Fractional numbers
- Binary point is set in fixed position, does not need to be stored in memory
How to convert recurring number to fixed point form
- Convert whole part of the number
- Multiply fractional part by 2
- Until fraction part is 0, already converted (repetition) or fraction space is full
Range of Unsigned Fixed Point Form numbers
1…1 to 0…01
Range of Signed Fixed Point Form numbers
01…1 to 0…01
Range of Negative Signed Fixed Point Form Numbers
10…0 to 1…1
Large number of bits for the whole part in floating point form results in
allows large values to be represented, but without the detail of the fractional part
Large number of bits for the fractional part results in
very small numbers yet increasingly precise values to be represented
Floating Point Forms are made from
- Mantissa
- Exponent
What to do with positive mantissa and negative exponent
- Find value and move point left by value
- Fill in with 0s
What to do with negative mantissa and positive exponent
-move right by value of exponent
What to do with negative mantissa and exponent
- Find value and move left by value
- Fill in with 1s
Define normalisation (Floating Point)
- Unique representation for a number
- Maximum possible precision
- Either 1.0, 0.1
How do you normalise
- One place to right (x2) reduce exponent by 1 (/2)
- One place to the left (/2) increase exponent by 1 (x2)
Define Underflow
Calculation result is too small to be represented with available number of bits