Notes/UNB/Year 5/Semester 1/CS3113/In class notes.md

## Convert numbers to binary
Number in decimal: 53.7
### Decimal conversion

| Calculation | Remainder/Binary |
| ----------- | ---------------- |
| 53 / 2 = 26 | 1                |
| 26 / 2 = 13 | 0                |
| 13 / 2 = 6  | 1                |
| 6 / 2 = 3   | 0                |
| 3 / 2 = 1   | 1                |
| 1 / 2 = 0   | 1                |
So in binary 110101, as the order is in reverse of the decimals
### Fraction Conversion

| Calculation   | Non Decimal Portion/Binary |
| ------------- | -------------------------- |
| 0.7 x 2 = 1.4 | 1                          |
| 0.4 x 2 = 0.8 | 0                          |
| 0.8 x 2 = 1.6 | 1                          |
| 0.6 x 2 = 1.2 | 1                          |
| 0.2 x 2 = 0.4 | 0                          |
And so on.. so the fraction would be .10110, with 0110 repeating infinitely
So the final number would be 110101.10110...

**Normalization** is the process is the process of adjusting a number so only 1 non zero digit on the left side of a number, i.e. the number is in scientific notation

## Floating point number types

| Precision   | Sign | Exponent | Mantissa |
| ----------- | ---- | -------- | -------- |
| single      | 1    | 8        | 23       |
| double      | 1    | 11       | 52       |
| long double | 1    | 15       | 64       |
Truncation types
**Chopping**: Omit the numbers that we don't want, looking to the first bit that we want to erase
**Rounding**: We should take care about the first digit that we want to omit and adjust the 52nd bit