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Add Full Adder algorithm (math/bits) (#334)

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* Add Full Adder algorithm (math/bits)

* Full adder: minor spelling fixes

* Full adder: even better comments
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Sergii Tkachenko
2019-04-03 00:42:16 -04:00
committed by Oleksii Trekhleb
parent 339ae02977
commit 97e4f5fe2a
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src/algorithms/math/bits/README.md
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@@ -226,6 +226,42 @@ Number: 9 = (10 - 1) = 0b01001
> See [isPowerOfTwo.js](isPowerOfTwo.js) for further details.
#### Full Adder
This method adds up two integer numbers using bitwise operators.
It implements [full adder](https://en.wikipedia.org/wiki/Adder_(electronics))
electronics circut logic to sum two 32-bit integers in two's complement format.
It's using the boolean logic to cover all possible cases of adding two input bits:
with and without a "carry bit" from adding the previous less-significant stage.
Legend:
- `A`: Number `A`
- `B`: Number `B`
- `ai`: ith bit of number `A`
- `bi`: ith bit of number `B`
- `carryIn`: a bit carried in from the previous less-significant stage
- `carryOut`: a bit to carry to the next most-significant stage
- `bitSum`: The sum of `ai`, `bi`, and `carryIn`
- `resultBin`: The full result of adding current stage with all less-significant stages (in binary)
- `resultBin`: The full result of adding current stage with all less-significant stages (in decimal)
```
A = 3: 011
B = 6: 110
┌──────┬────┬────┬─────────┬──────────┬─────────┬───────────┬───────────┐
│ bit │ ai │ bi │ carryIn │ carryOut │ bitSum │ resultBin │ resultDec │
├──────┼────┼────┼─────────┼──────────┼─────────┼───────────┼───────────┤
│ 0 │ 1 │ 0 │ 0 │ 0 │ 1 │ 1 │ 1 │
│ 1 │ 1 │ 1 │ 0 │ 1 │ 0 │ 01 │ 1 │
│ 2 │ 0 │ 1 │ 1 │ 1 │ 0 │ 001 │ 1 │
│ 3 │ 0 │ 0 │ 1 │ 0 │ 1 │ 1001 │ 9 │
└──────┴────┴────┴─────────┴──────────┴─────────┴───────────┴───────────┘
```
> See [fullAdder.js](fullAdder.js) for further details.
> See [Full Adder on YouTube](https://www.youtube.com/watch?v=wvJc9CZcvBc).
## References
- [Bit Manipulation on YouTube](https://www.youtube.com/watch?v=NLKQEOgBAnw&t=0s&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)