Skip to content

Navigation Menu

Sign in
Appearance settings

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly
Sign up
Appearance settings

Commit 97e4f5f

Browse files
sergiitktrekhleb
authored andcommitted
Add Full Adder algorithm (math/bits) (trekhleb#334)
* Add Full Adder algorithm (math/bits) * Full adder: minor spelling fixes * Full adder: even better comments
1 parent 339ae02 commit 97e4f5f

File tree

3 files changed

+123
-0
lines changed

3 files changed

+123
-0
lines changed

‎src/algorithms/math/bits/README.md

Lines changed: 36 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -226,6 +226,42 @@ Number: 9 = (10 - 1) = 0b01001
226226

227227
> See [isPowerOfTwo.js](isPowerOfTwo.js) for further details.
228228
229+
230+
#### Full Adder
231+
232+
This method adds up two integer numbers using bitwise operators.
233+
234+
It implements [full adder](https://en.wikipedia.org/wiki/Adder_(electronics))
235+
electronics circut logic to sum two 32-bit integers in two's complement format.
236+
It's using the boolean logic to cover all possible cases of adding two input bits:
237+
with and without a "carry bit" from adding the previous less-significant stage.
238+
239+
Legend:
240+
- `A`: Number `A`
241+
- `B`: Number `B`
242+
- `ai`: ith bit of number `A`
243+
- `bi`: ith bit of number `B`
244+
- `carryIn`: a bit carried in from the previous less-significant stage
245+
- `carryOut`: a bit to carry to the next most-significant stage
246+
- `bitSum`: The sum of `ai`, `bi`, and `carryIn`
247+
- `resultBin`: The full result of adding current stage with all less-significant stages (in binary)
248+
- `resultBin`: The full result of adding current stage with all less-significant stages (in decimal)
249+
```
250+
A = 3: 011
251+
B = 6: 110
252+
┌──────┬────┬────┬─────────┬──────────┬─────────┬───────────┬───────────┐
253+
│ bit │ ai │ bi │ carryIn │ carryOut │ bitSum │ resultBin │ resultDec │
254+
├──────┼────┼────┼─────────┼──────────┼─────────┼───────────┼───────────┤
255+
│ 0 │ 1 │ 0 │ 0 │ 0 │ 1 │ 1 │ 1 │
256+
│ 1 │ 1 │ 1 │ 0 │ 1 │ 0 │ 01 │ 1 │
257+
│ 2 │ 0 │ 1 │ 1 │ 1 │ 0 │ 001 │ 1 │
258+
│ 3 │ 0 │ 0 │ 1 │ 0 │ 1 │ 1001 │ 9 │
259+
└──────┴────┴────┴─────────┴──────────┴─────────┴───────────┴───────────┘
260+
```
261+
262+
> See [fullAdder.js](fullAdder.js) for further details.
263+
> See [Full Adder on YouTube](https://www.youtube.com/watch?v=wvJc9CZcvBc).
264+
229265
## References
230266

231267
- [Bit Manipulation on YouTube](https://www.youtube.com/watch?v=NLKQEOgBAnw&t=0s&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
Lines changed: 18 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,18 @@
1+
import fullAdder from '../fullAdder';
2+
3+
describe('Full adder', () => {
4+
it('should add up two numbers', () => {
5+
expect(fullAdder(0, 0)).toBe(0);
6+
expect(fullAdder(2, 0)).toBe(2);
7+
expect(fullAdder(0, 2)).toBe(2);
8+
expect(fullAdder(1, 2)).toBe(3);
9+
expect(fullAdder(2, 1)).toBe(3);
10+
expect(fullAdder(6, 6)).toBe(12);
11+
expect(fullAdder(-2, 4)).toBe(2);
12+
expect(fullAdder(4, -2)).toBe(2);
13+
expect(fullAdder(-4, -4)).toBe(-8);
14+
expect(fullAdder(4, -5)).toBe(-1);
15+
expect(fullAdder(2, 121)).toBe(123);
16+
expect(fullAdder(121, 2)).toBe(123);
17+
});
18+
});

‎src/algorithms/math/bits/fullAdder.js

Lines changed: 69 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,69 @@
1+
import getBit from './getBit';
2+
3+
/**
4+
* Add two numbers using only binary operators.
5+
*
6+
* This is an implementation of full adders logic circut.
7+
* https://en.wikipedia.org/wiki/Adder_(electronics)
8+
* Inspired by: https://www.youtube.com/watch?v=wvJc9CZcvBc
9+
*
10+
* Table(1)
11+
* INPUT | OUT
12+
* C Ai Bi | C Si | Row
13+
* -------- | -----| ---
14+
* 0 0 0 | 0 0 | 1
15+
* 0 0 1 | 0 1 | 2
16+
* 0 1 0 | 0 1 | 3
17+
* 0 1 1 | 1 0 | 4
18+
* -------- | ---- | --
19+
* 1 0 0 | 0 1 | 5
20+
* 1 0 1 | 1 0 | 6
21+
* 1 1 0 | 1 0 | 7
22+
* 1 1 1 | 1 1 | 8
23+
* ---------------------
24+
*
25+
* Legend:
26+
* INPUT C = Carry in, from the previous less-significant stage
27+
* INPUT Ai = ith bit of Number A
28+
* INPUT Bi = ith bit of Number B
29+
* OUT C = Carry out to the next most-significant stage
30+
* OUT Si = Bit Sum, ith least significant bit of the result
31+
*
32+
*
33+
* @param {number} a
34+
* @param {number} b
35+
* @return {number}
36+
*/
37+
export default function fullAdder(a, b) {
38+
let result = 0;
39+
let carry = 0;
40+
41+
// The operands of all bitwise operators are converted to signed
42+
// 32-bit integers in two's complement format.
43+
// https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Bitwise_Operators#Signed_32-bit_integers
44+
for (let i = 0; i < 32; i += 1) {
45+
const ai = getBit(a, i);
46+
const bi = getBit(b, i);
47+
const carryIn = carry;
48+
49+
// Calculate binary Ai + Bi without carry (half adder)
50+
// See Table(1) rows 1 - 4: Si = Ai ^ Bi
51+
const aiPlusBi = ai ^ bi;
52+
53+
// Calculate ith bit of the result by adding the carry bit to Ai + Bi
54+
// For Table(1) rows 5 - 8 carryIn = 1: Si = Ai ^ Bi ^ 1, flip the bit
55+
// Fpr Table(1) rows 1 - 4 carryIn = 0: Si = Ai ^ Bi ^ 0, a no-op.
56+
const bitSum = aiPlusBi ^ carryIn;
57+
58+
// Carry out one to the next most-significant stage
59+
// when at least one of these is true:
60+
// 1) Table(1) rows 6, 7: one of Ai OR Bi is 1 AND carryIn = 1
61+
// 2) Table(1) rows 4, 8: Both Ai AND Bi are 1
62+
const carryOut = (aiPlusBi & carryIn) | (ai & bi);
63+
carry = carryOut;
64+
65+
// Set ith least significant bit of the result to bitSum.
66+
result |= bitSum << i;
67+
}
68+
return result;
69+
}

0 commit comments

Comments
(0)

AltStyle によって変換されたページ (->オリジナル) /