37 lines
1.5 KiB
Markdown
37 lines
1.5 KiB
Markdown
e hn## Convert numbers to binary
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Number in decimal: 53.7
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### Decimal conversion
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| Calculation | Remainder/Binary |
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| ----------- | ---------------- |
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| 53 / 2 = 26 | 1 |
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| 26 / 2 = 13 | 0 |
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| 13 / 2 = 6 | 1 |
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| 6 / 2 = 3 | 0 |
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| 3 / 2 = 1 | 1 |
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| 1 / 2 = 0 | 1 |
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So in binary 110101, as the order is in reverse of the decimals
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### Fraction Conversion
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| Calculation | Non Decimal Portion/Binary |
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| ------------- | -------------------------- |
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| 0.7 x 2 = 1.4 | 1 |
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| 0.4 x 2 = 0.8 | 0 |
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| 0.8 x 2 = 1.6 | 1 |
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| 0.6 x 2 = 1.2 | 1 |
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| 0.2 x 2 = 0.4 | 0 |
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And so on.. so the fraction would be .10110, with 0110 repeating infinitely
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So the final number would be 110101.10110...
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**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
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## Floating point number types
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| Precision | Sign | Exponent | Mantissa |
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| ----------- | ---- | -------- | -------- |
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| single | 1 | 8 | 23 |
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| double | 1 | 11 | 52 |
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| long double | 1 | 15 | 64 |
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Truncation types
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**Chopping**: Omit the numbers that we don't want, looking to the first bit that we want to erase
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**Rounding**: We should take care about the first digit that we want to omit and adjust the 52nd bit |