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Commit97e4f5f

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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
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‎src/algorithms/math/bits/README.md

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>See[isPowerOfTwo.js](isPowerOfTwo.js) for further details.
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####Full Adder
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This method adds up two integer numbers using bitwise operators.
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It implements[full adder](https://en.wikipedia.org/wiki/Adder_(electronics))
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electronics circut logic to sum two 32-bit integers in two's complement format.
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It's using the boolean logic to cover all possible cases of adding two input bits:
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with and without a "carry bit" from adding the previous less-significant stage.
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Legend:
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-`A`: Number`A`
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-`B`: Number`B`
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-`ai`: ith bit of number`A`
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-`bi`: ith bit of number`B`
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-`carryIn`: a bit carried in from the previous less-significant stage
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-`carryOut`: a bit to carry to the next most-significant stage
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-`bitSum`: The sum of`ai`,`bi`, and`carryIn`
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-`resultBin`: The full result of adding current stage with all less-significant stages (in binary)
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-`resultBin`: The full result of adding current stage with all less-significant stages (in decimal)
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```
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A = 3: 011
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B = 6: 110
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┌──────┬────┬────┬─────────┬──────────┬─────────┬───────────┬───────────┐
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│ bit │ ai │ bi │ carryIn │ carryOut │ bitSum │ resultBin │ resultDec │
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├──────┼────┼────┼─────────┼──────────┼─────────┼───────────┼───────────┤
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│ 0 │ 1 │ 0 │ 0 │ 0 │ 1 │ 1 │ 1 │
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│ 1 │ 1 │ 1 │ 0 │ 1 │ 0 │ 01 │ 1 │
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│ 2 │ 0 │ 1 │ 1 │ 1 │ 0 │ 001 │ 1 │
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│ 3 │ 0 │ 0 │ 1 │ 0 │ 1 │ 1001 │ 9 │
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└──────┴────┴────┴─────────┴──────────┴─────────┴───────────┴───────────┘
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```
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>See[fullAdder.js](fullAdder.js) for further details.
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>See[Full Adder on YouTube](https://www.youtube.com/watch?v=wvJc9CZcvBc).
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##References
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-[Bit Manipulation on YouTube](https://www.youtube.com/watch?v=NLKQEOgBAnw&t=0s&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
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importfullAdderfrom'../fullAdder';
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describe('Full adder',()=>{
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it('should add up two numbers',()=>{
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expect(fullAdder(0,0)).toBe(0);
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expect(fullAdder(2,0)).toBe(2);
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expect(fullAdder(0,2)).toBe(2);
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expect(fullAdder(1,2)).toBe(3);
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expect(fullAdder(2,1)).toBe(3);
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expect(fullAdder(6,6)).toBe(12);
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expect(fullAdder(-2,4)).toBe(2);
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expect(fullAdder(4,-2)).toBe(2);
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expect(fullAdder(-4,-4)).toBe(-8);
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expect(fullAdder(4,-5)).toBe(-1);
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expect(fullAdder(2,121)).toBe(123);
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expect(fullAdder(121,2)).toBe(123);
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});
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});

‎src/algorithms/math/bits/fullAdder.js

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importgetBitfrom'./getBit';
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/**
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* Add two numbers using only binary operators.
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*
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* This is an implementation of full adders logic circut.
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* https://en.wikipedia.org/wiki/Adder_(electronics)
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* Inspired by: https://www.youtube.com/watch?v=wvJc9CZcvBc
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*
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* Table(1)
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* INPUT | OUT
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* C Ai Bi | C Si | Row
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* -------- | -----| ---
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* 0 0 0 | 0 0 | 1
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* 0 0 1 | 0 1 | 2
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* 0 1 0 | 0 1 | 3
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* 0 1 1 | 1 0 | 4
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* -------- | ---- | --
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* 1 0 0 | 0 1 | 5
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* 1 0 1 | 1 0 | 6
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* 1 1 0 | 1 0 | 7
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* 1 1 1 | 1 1 | 8
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* ---------------------
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*
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* Legend:
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* INPUT C = Carry in, from the previous less-significant stage
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* INPUT Ai = ith bit of Number A
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* INPUT Bi = ith bit of Number B
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* OUT C = Carry out to the next most-significant stage
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* OUT Si = Bit Sum, ith least significant bit of the result
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*
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*
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*@param {number} a
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*@param {number} b
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*@return {number}
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*/
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exportdefaultfunctionfullAdder(a,b){
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letresult=0;
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letcarry=0;
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// The operands of all bitwise operators are converted to signed
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// 32-bit integers in two's complement format.
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// https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Bitwise_Operators#Signed_32-bit_integers
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for(leti=0;i<32;i+=1){
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constai=getBit(a,i);
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constbi=getBit(b,i);
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constcarryIn=carry;
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// Calculate binary Ai + Bi without carry (half adder)
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// See Table(1) rows 1 - 4: Si = Ai ^ Bi
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constaiPlusBi=ai^bi;
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// Calculate ith bit of the result by adding the carry bit to Ai + Bi
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// For Table(1) rows 5 - 8 carryIn = 1: Si = Ai ^ Bi ^ 1, flip the bit
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// Fpr Table(1) rows 1 - 4 carryIn = 0: Si = Ai ^ Bi ^ 0, a no-op.
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constbitSum=aiPlusBi^carryIn;
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// Carry out one to the next most-significant stage
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// when at least one of these is true:
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// 1) Table(1) rows 6, 7: one of Ai OR Bi is 1 AND carryIn = 1
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// 2) Table(1) rows 4, 8: Both Ai AND Bi are 1
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constcarryOut=(aiPlusBi&carryIn)|(ai&bi);
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carry=carryOut;
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// Set ith least significant bit of the result to bitSum.
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result|=bitSum<<i;
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}
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returnresult;
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}

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