1.7 KiB
1.7 KiB
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 |
Machine Epsilon: Difference between the smallest floating point number greater than 1 and 1, ie the smallest number that when added to 1, will be different than 1