// 常规位运算// https://developer.mozilla.org/zh-CN/docs/Web/JavaScript/Reference/Operators/Bitwise_Operatorsconst AND = (a, b) => a & b;const OR = (a, b) => a | b;const XOR = (a, b) => a ^ b;const NOT = a => ~a;// Fake Node Assert Libconst assert = { deepEqual: (a, b) => { if (a.toString() === b.toString()) return; throw new Error(`Not Equal: ${a} ${b}`); }}半加器
/ 半加器 两个 bit 输入，输出数组 [进位，和] 如： 1,1 => [1, 0] @param {bit} a 输入 @param {bit} b 输入 /const HalfAdder = (a, b) => [a & b, a ^ b];// 半加器测试assert.deepEqual(HalfAdder(0, 0), [0, 0]);assert.deepEqual(HalfAdder(0, 1), [0, 1]);assert.deepEqual(HalfAdder(1, 0), [0, 1]);assert.deepEqual(HalfAdder(1, 1), [1, 0]);全加器
/ 全加器 两个 bit 输入，和进位输入，输出数组 [进位，和] 如： 0,1,1 => [1, 0] @param {bit} a 输入 @param {bit} b 输入 @param {bit} c 进位输入 /const FullAdder = (a, b, c) => { var t1 = HalfAdder(a, b); var t2 = HalfAdder(t1[1], c); return [t1[0] | t2[0], t2[1]];}// 全加器测试assert.deepEqual(FullAdder(0, 0, 0), [0, 0]);assert.deepEqual(FullAdder(1, 0, 0), [0, 1]);assert.deepEqual(FullAdder(0, 1, 0), [0, 1]);assert.deepEqual(FullAdder(0, 0, 1), [0, 1]);assert.deepEqual(FullAdder(1, 1, 0), [1, 0]);assert.deepEqual(FullAdder(1, 0, 1), [1, 0]);assert.deepEqual(FullAdder(0, 1, 1), [1, 0]);assert.deepEqual(FullAdder(1, 1, 1), [1, 1]);波纹进位加法器
/ 波纹加法器， 4 位加法器 如： [0, 1, 0, 1],[0, 1, 0, 1] => [1, 0, 1, 0] @param {Array<Number>} a 4位 bit 输入数组，如：[0, 1, 0, 1] @param {Array<Number>} b 4位 bit 输入数组，如：[0, 1, 0, 1] @returns {Array<Number>} /const RippleCarryAdder = (a, b) => { let carry = 0; let bit = 3; let result = []; while(bit >= 0) { let temp = FullAdder(a[bit], b[bit], carry); carry = temp[0]; result.push(temp[1]); bit--; } return result.reverse();}/ 将数字转成 4 位二进制数组 如： 1 => [0, 0, 0, 1] 3 => [0, 0, 1, 1] @param {Number} a 数字 @returns {Array<Number>} /const to4Bit = a => ( a.toString(2) .split('') .reverse() .concat(Array(4).fill('0')) .slice(0,4) .reverse() .map(i => +i));/ 将二进制字符串转为数字 如： '1010' => 10 @param {String} a 4 位二进制字符串 @returns {Number} /const from4Bit = a => parseInt(a, 2);/ 加法简写工具 @param {Number} a 输入 @param {Number} b 输入 /const helper = (a, b) => ( from4Bit(RippleCarryAdder( to4Bit(a), to4Bit(b) ).join('')))assert.deepEqual(helper(0, 0), 0);assert.deepEqual(helper(1, 1), 2);assert.deepEqual(helper(1, 2), 3);assert.deepEqual(helper(2, 2), 4);assert.deepEqual(helper(3, 5), 8);assert.deepEqual(helper(1, 14), 15);// 9 + 14 为 23，但由于我们写的是 4 位加法器，以是有溢出// 终极的结果须要 mod 0x10（也便是 16）assert.deepEqual(helper(9, 14), 23 % 0x10);assert.deepEqual(helper(9, 14), 7);关于补码 & 减法
我们以 4 bit 存储数字，并以最高位作为符号位
2 - 1 = 2 + (- 1) = 0010（补）+ 1111（补）= 0010（补）= 17 % 16 = 12 - 3 = 2 + (- 3) = 0010（补）+ 1101（补）= 1111（补）= 15 % 16 = -1
