在重溫《編碼：隱匿在計算機軟硬件背后的語言》第12章——二進制加法器時，心血來潮用JS寫了一個模擬串行加法器。

測試斷言工具TestUtils.js

function assertTrue(actual){if(!actual)throw "Error actual: " + actual + " is not true." }function assertFalse(actual){if(actual)throw "Error actual: " + actual + " is not false." }function assertIntEquals(expected, actual){if(typeof expected != "number")throw "Error expected: " + expected +" is not a number."if(typeof actual != "number")throw "Error actual: " + actual +" is not a number."if(expected != actual)throw "Error expected: " + expected + " and actual: " + actual +" is different." }

十進制數與二進制數之間轉換工具utils.js

function int2LowEightBitArray(num){var result = []for(var i = 0; i < 8; i++)result.push(((num >> i) & 1) == 1)return result }function lowEightBitArray2Int(array){var result = 0for(var i = 0; i < 8; i++){if(array[i])result += (1 << i)}return result }function lowNineBitArray2Int(array){var result = 0for(var i = 0; i < 9; i++){if(array[i])result += (1 << i)}return result }//用補碼表示負數 function int2EightBitArray(num){if(num < -128 || num > 127){throw "Out of boundary(-128, 127)."}var result = []for(var i = 0; i < 8; i++)result.push(((num >> i) & 1) == 1)return result }function eightBitArray2Int(array){var result = 0for(var i = 0; i < 7; i++){if(array[i])result += (1 << i)}if(array[i])result += -128return result }function int2SixteenBitArray(num){if(num < -(1 << 15) || num > (1 << 15) - 1){throw "Out of boundary({left}, {right}).".replace("{left}", -(1 << 15)).replace("{right}", (1 << 15) - 1)}var result = []for(var i = 0; i < 16; i++)result.push(((num >> i) & 1) == 1)return result }function sixteentBitArray2Int(array){var result = 0for(var i = 0; i < 15; i++){if(array[i])result += (1 << i)}if(array[i])result += -(1 << 15)return result }

加法器模型model.js

class DoubleInGate{#id#in1#in2#gateTypeName#func#out#lastOut#outReceiver#outReceiverInNameconstructor(id, gateTypeName, in1 = false, in2 = false, func){this.#id = idthis.#gateTypeName = gateTypeNamethis.#in1 = in1this.#in2 = in2this.#func = functhis.#out = this.#func(this.in1, this.in2)// this.#lastOut = this.#out}updateIn1(flag){this.#in1 = flagthis.#updateOut()}updateIn2(flag){this.#in2 = flagthis.#updateOut()}getOut(){return this.#out;}updateBothIn(in1 = false, in2 = false){this.#in1 = in1this.#in2 = in2this.#updateOut()}setOutReceiver(outReceiver, inName){this.#outReceiver = outReceiverthis.#outReceiverInName = inName}#updateOut(){this.#lastOut = this.#outthis.#out = this.#func(this.#in1, this.#in2)if(this.#out != this.#lastOut){this.#send(this.#out)}}#send(flag){if(this.#outReceiver){this.#outReceiver.receive(this.#outReceiverInName, flag)}}receive(inName, flag){if(inName == "in1"){this.updateIn1(flag)}else if(inName == "in2"){this.updateIn2(flag)}}toString(){return "{gateTypeName} id: {id}, in1: {in1}, in2: {in2}, out:{out}".replace("{gateTypeName}", this.#gateTypeName).replace("{id}", this.#id).replace("{in1}", this.#in1).replace("{in2}", this.#in2).replace("{out}", this.#out)} }//與門 class AndGate extends DoubleInGate{constructor(id, in1 = false, in2 = false){super(id, "AndGate", in1, in2, (i1, i2) => i1 && i2)} }//或門 class OrGate extends DoubleInGate{constructor(id, in1 = false, in2 = false){super(id, "OrGate", in1, in2, (i1, i2) => i1 || i2)} }//異或門 class XorGate extends DoubleInGate{constructor(id, in1 = false, in2 = false){//^在js按位異或, 而在java中不是super(id, "XorGate", in1, in2, (i1, i2) => (i1 || i2) && !(i1 && i2)) } }class SingleInGate{#id#in#out#lastOut#func#outReceiver#outReceiverInNameconstructor(id, in_, func){this.#id = idthis.#in = in_this.#func = functhis.#out = this.#func(this.#in)// this.#lastOut = this.#out}updateIn(flag){this.#in = flagthis.#updateOut()}getOut(){return this.#out}//注冊輸出端口接收者，（類觀察者模式）setOutReceiver(outReceiver, inName){this.#outReceiver = outReceiverthis.#outReceiverInName = inName}#updateOut(){this.#lastOut = this.#outthis.#out = this.#func(this.#in)if(this.#out != this.#lastOut){this.#send(this.#out)}}#send(flag){if(this.#outReceiver){this.#outReceiver.receive(this.#outReceiverInName, flag)} }receive(inName, flag){if(inName == "in"){ //TODO 或許有更靈活的寫法this.updateIn(flag)}} }class NullGate extends SingleInGate{constructor(id, in_= false){super(id, in_, a=>a)} }class NotGate extends SingleInGate{constructor(id, in_= false){super(id, in_, a=>!a)} }class Adder{#id#inA#inB#outS#outC#lastOutS#lastOutC#outSReceiver#outSReceiverInName#outCReceiver#outCReceiverInNameconstructor(id, inA=false, inB=false, outS, outC){this.#id = idthis.#inA = inAthis.#inB = inBthis.#outS = outSthis.#outC = outC}updateInA(flag, func){this.#inA = flagthis.updateOutSAndOutC(func)}updateInB(flag, func){this.#inB = flagthis.updateOutSAndOutC(func)}updateBothIn(inA, inB, func){this.#inA = inAthis.#inB = inBthis.updateOutSAndOutC(func)}getOutS(){return this.#outS}getOutC(){return this.#outC}#updateOutS(flag){this.#lastOutS = this.#outSthis.#outS = flagif(this.#outS != this.#lastOutS){this.#sendOutS(this.#outS)}}#updateOutC(flag){this.#lastOutC = this.#outCthis.#outC = flagif(this.#outC != this.#lastOutC){this.#sendOutC(this.#outC)}}updateOutSAndOutC(func){if(func){var results = func()this.#updateOutS(results[0])this.#updateOutC(results[1])}}setOutSReceiver(outSReceiver, inName){this.#outSReceiver = outSReceiverthis.#outSReceiverInName = inName}setOutCReceiver(outCReceiver, inName){this.#outCReceiver = outCReceiverthis.#outCReceiverInName = inName}receive(inName, flag){if(inName == "inA"){this.updateInA(flag)}else if(inName == "inB"){this.updateInB(flag)}}#sendOutS(flag){if(this.#outSReceiver){this.#outSReceiver.receive(this.#outSReceiverInName, flag)}}#sendOutC(flag){if(this.#outCReceiver){this.#outCReceiver.receive(this.#outCReceiverInName, flag)}} }class HalfAdder extends Adder{#xorGate#andGateconstructor(id, inA=false, inB=false){var xorGate = new XorGate(undefined, inA, inB);var andGate = new AndGate(undefined, inA, inB);super(id, inA, inB, xorGate.getOut(), andGate.getOut())this.#xorGate = xorGatethis.#andGate = andGate }#returnOutArray(){return [this.#xorGate.getOut(), this.#andGate.getOut()]}updateInA(flag){super.updateInA(flag, ()=>{this.#xorGate.updateIn1(flag)this.#andGate.updateIn1(flag)return this.#returnOutArray()})}updateInB(flag){super.updateInB(flag, ()=>{this.#xorGate.updateIn2(flag)this.#andGate.updateIn2(flag)return this.#returnOutArray()})}updateBothIn(inA, inB){super.updateBothIn(inA, inB, ()=>{this.#xorGate.updateBothIn(inA, inB)this.#andGate.updateBothIn(inA, inB)return this.#returnOutArray()})}}class FullAdder extends Adder{#inC#halfAdder1#halfAdder2#orGateconstructor(id, inA = false, inB = false, inC = false){var halfAdder1 = new HalfAdder(undefined, inA, inB)var halfAdder2 = new HalfAdder(undefined, inC, halfAdder1.getOutS())var orGate = new OrGate(undefined, halfAdder1.getOutC(), halfAdder2.getOutC())super(id, inA, inB, halfAdder2.getOutS(), orGate.getOut())this.#inC = inCthis.#halfAdder1 = halfAdder1this.#halfAdder2 = halfAdder2this.#orGate = orGatethis.#halfAdder1.setOutSReceiver(halfAdder2, "inB")this.#halfAdder1.setOutCReceiver(orGate, "in1")this.#halfAdder2.setOutCReceiver(orGate, "in2")}#returnOutArray(){return [this.#halfAdder2.getOutS(), this.#orGate.getOut()]}updateInA(flag){super.updateInA(flag, ()=>{this.#halfAdder1.updateInA(flag)return this.#returnOutArray()})}updateInB(flag){super.updateInB(flag, ()=>{this.#halfAdder1.updateInB(flag)return this.#returnOutArray()})}updateInC(flag){this.#inC = flagthis.#halfAdder2.updateInA(flag)this.updateOutSAndOutC(()=>{return this.#returnOutArray()})}updateBothIn(inA, inB){super.updateBothIn(inA, inB, ()=>{this.#halfAdder1.updateBothIn(inA, inB)return this.#returnOutArray()})}updateThreeIn(inA, inB, inC){super.updateBothIn(inA, inB)this.#inC = inCthis.#halfAdder1.updateBothIn(inA, inB)this.#halfAdder2.updateBothIn(inC, this.#halfAdder1.getOutS())this.#orGate.updateBothIn(this.#halfAdder1.getOutC(), this.#halfAdder2.getOutC())this.updateOutSAndOutC(()=>{return this.#returnOutArray()})}receive(inName, flag){super.receive(inName, flag)if(inName == "inC"){this.updateInC(flag)}} }class EightBitBinaryAdder{#inC#outC#lastOutC#inA#inB#outS#fullAdders#fullAdderNum#outCReceiver#outCReceiverInName#outCInOutSFlagconstructor(outCInOutSFlag = false){this.#outCInOutSFlag = outCInOutSFlagthis.#inC = falsethis.#fullAdderNum = 8this.#fullAdders = []this.#inA = []this.#inB = []for(var i = 0; i < this.#fullAdderNum; i++){this.#inA.push(false)this.#inB.push(false)}//新鍵8個全加器for(var i = 0; i < this.#fullAdderNum; i++){this.#fullAdders.push(new FullAdder("f" + i))if(i != 0){this.#fullAdders[i - 1].setOutCReceiver(this.#fullAdders[i], "inC")}}this.updateOut()}updateBothIn(arrayA, arrayB){// this.#inC = inCthis.#inA = arrayAthis.#inB = arrayBfor(var i = 0; i < this.#fullAdderNum; i++){if(i == 0){this.#fullAdders[i].updateInC(this.#inC)}this.#fullAdders[i].updateBothIn(arrayA[i], arrayB[i])}this.updateOut()}//輸出默認值updateOut(){this.#outS = []for(var i = 0; i < this.#fullAdderNum; i++){this.#outS.push(this.#fullAdders[i].getOutS())if(i == this.#fullAdderNum - 1){this.#lastOutC = this.#outCthis.#outC = this.#fullAdders[i].getOutC()if(this.#lastOutC != this.#outC)this.#sendOutC(this.#outC)if(this.#outCInOutSFlag)this.#outS.push(this.#outC)}}}updateInC(flag){this.#inC = flagthis.updateBothIn(this.#inA, this.#inB, flag)}receive(inName, flag){if(inName == "inC"){this.updateInC(flag)}}#sendOutC(flag){if(this.#outCReceiver){this.#outCReceiver.receive(this.#outCReceiverInName, flag)}}setOutCReceiver(outCReceiver, inName){this.#outCReceiver = outCReceiverthis.#outCReceiverInName = inName}getOut(){return this.#outS} }class SixteenBitBinaryAdder{#inC#outC#lastOutC#inA#inB#outS#eightBitBinaryAdder1#eightBitBinaryAdder2#bitNum = 16#outCReceiver#outCReceiverInName#outCInOutSFlagconstructor(outCInOutSFlag){this.#outCInOutSFlag = outCInOutSFlagthis.#inC = falsethis.#eightBitBinaryAdder1 = new EightBitBinaryAdder()this.#eightBitBinaryAdder2 = new EightBitBinaryAdder()this.#inA = []this.#inB = []for(var i = 0; i < this.#bitNum; i++){this.#inA.push(false)this.#inB.push(false)}this.#eightBitBinaryAdder1.setOutCReceiver(this.#eightBitBinaryAdder2, "inC")this.updateOut()}updateBothIn(arrayA, arrayB){this.#inA = arrayAthis.#inB = arrayBthis.#eightBitBinaryAdder1.updateBothIn(arrayA.slice(0, 8), arrayB.slice(0, 8))this.#eightBitBinaryAdder2.updateBothIn(arrayA.slice(8), arrayB.slice(8))this.updateOut()}updateOut(){this.#outS = this.#eightBitBinaryAdder1.getOut().concat(this.#eightBitBinaryAdder2.getOut())//發送send(OutC)}getOut(){return this.#outS}//TODO// updateInC(flag){// this.#inC = flag// this.updateBothIn(this.#inA, this.#inB, flag)// }// receive(inName, flag){// if(inName == "inC"){// this.updateInC(flag)// }// }#sendOutC(flag){if(this.#outCReceiver){this.#outCReceiver.receive(this.#outCReceiverInName, flag)}}setOutCReceiver(outCReceiver, inName){this.#outCReceiver = outCReceiverthis.#outCReceiverInName = inName}}

運行驗證代碼

驗證通過判據：后臺沒有打印輸出異常。

<!DOCTYPE html> <html lang="en"> <head><meta charset="UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Test</title><script src="../js/test/TestUtils.js"></script><script src="../js/model.js"></script><script src="../js/utils.js"></script> </head> <body><script>var g1 = new NullGate("g1")var g2 = new NullGate("g2")var g3 = new NullGate("g3")var g4 = new NullGate("g4")var g5 = new NullGate("g5")var g6 = new NullGate("g6")g1.setOutReceiver(g2, "in")g2.setOutReceiver(g3, "in")g3.setOutReceiver(g4, "in")g4.setOutReceiver(g5, "in")g5.setOutReceiver(g6, "in")g1.updateIn(true)assertTrue(g6.getOut())</script><script>//與門var andGate = new AndGate("a01")assertFalse(andGate.getOut())andGate.updateIn1(true)assertFalse(andGate.getOut())andGate.updateIn2(true)assertTrue(andGate.getOut())//或門var orGate = new OrGate("o01")assertFalse(orGate.getOut())orGate.updateIn1(true)assertTrue(orGate.getOut())orGate.updateIn2(true)assertTrue(orGate.getOut())//異或門var xorGate = new XorGate("x01")assertFalse(xorGate.getOut())xorGate.updateIn1(true)assertTrue(xorGate.getOut())xorGate.updateIn2(true)assertFalse(xorGate.getOut())xorGate.updateBothIn(false, true)assertTrue(xorGate.getOut())</script><script>//半加器var ha = new HalfAdder("h01")assertFalse(ha.getOutS())assertFalse(ha.getOutC())ha.updateInB(true)assertTrue(ha.getOutS())assertFalse(ha.getOutC())ha.updateInA(true)assertFalse(ha.getOutS())assertTrue(ha.getOutC())ha.updateBothIn(true, false)assertTrue(ha.getOutS())assertFalse(ha.getOutC())</script><script>//全加器var fa = new FullAdder("fa01")assertFalse(fa.getOutC())assertFalse(fa.getOutS())function test(inA, inB, inC, expectedS, expectedC){fa.updateThreeIn(inA, inB, inC)if(expectedS)assertTrue(fa.getOutS())elseassertFalse(fa.getOutS())if(expectedC)assertTrue(fa.getOutC())elseassertFalse(fa.getOutC())}test(false, false, false, false, false)test(false, true, false, true, false)test(true, false, false, true, false)test(true, true, false, false, true)test(false, false, true, true, false)test(false, true, true, false, true)test(true, false, true, false, true)test(true, true, true, true, true)</script><script>for(var i = 0 ; i < 256; i++){assertIntEquals(i, lowEightBitArray2Int(int2LowEightBitArray(i)))}</script><script>var ebba = new EightBitBinaryAdder(true)for(var i = 0; i < 256; i++){for(var j = 0; j < 256; j++){iebba.updateBothIn(int2LowEightBitArray(i), int2LowEightBitArray(j))assertIntEquals(i + j, lowNineBitArray2Int(ebba.getOut()))}}</script><script>for(var i = -128; i <= 127; i++){assertIntEquals(i, eightBitArray2Int(int2EightBitArray(i)))}</script><script>var ebba = new EightBitBinaryAdder()for(var i = -64; i < 64; i++){for(var j = -64; j < 64; j++){ebba.updateBothIn(int2EightBitArray(i), int2EightBitArray(j))assertIntEquals(i + j, eightBitArray2Int(ebba.getOut()))}}</script><script>for(var i = -(1<<15); i <= (1<<15) - 1; i++){assertIntEquals(i, sixteentBitArray2Int(int2SixteenBitArray(i)))}</script><script>var sbba = new SixteenBitBinaryAdder()sbba.updateBothIn(int2SixteenBitArray(1156), int2SixteenBitArray(9999))assertIntEquals(9999 + 1156, sixteentBitArray2Int(sbba.getOut()))//?16384? * ?16384? = 268435456 如果這樣算會十分耗時// for(var i = -(1<<14); i < (1<<14); i++){// for(var j = -(1<<14); j < (1<<14); j++){// sbba.updateBothIn(int2SixteenBitArray(i), int2SixteenBitArray(j))// assertIntEquals(i + j, sixteentBitArray2Int(sbba.getOut()))// }// }for(var i = -100; i < 100; i++){for(var j = -100; j < 100; j++){sbba.updateBothIn(int2SixteenBitArray(i), int2SixteenBitArray(j))assertIntEquals(i + j, sixteentBitArray2Int(sbba.getOut()))}}</script> </body> </html>

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