35 binary adder

adder.js

// a half-adder takes 2 binary bits as input, and return as result the sum and carry flag
function halfAdder(a, b) {
  // the sum is 0 when two bits are the same (1 + 1 or 0 + 0)
  var s = a ^ b
  // the carry flag is set when 1 + 1
  // the bitwise expression !(a ^ b) is for testing equality between a and b
  var c = !(a ^ 1) && (!a ^ b)
  return [c, s]
}

// a full-adder takes 2 binary bits and a carry flag as input,
// and return as result the sum and the carry flag after summation
function fullAdder(a, b, cin) {
  var [c2, tsum] = halfAdder(b, cin)
  var [c1, sum] = halfAdder(a, tsum)
  var cout = c1 | c2
  return [cout, sum]
}

// a full-adder can be use to add two numbers in 1 bit
// a sequence of full-adders in cascade can be use to add two numbers in N bits
function binaryAdder(addend, augend) {
  addend = addend.split('').map((digit) => {
    return parseInt(digit)
  })
  augend = augend.split('').map((digit) => {
    return parseInt(digit)
  })
  return baHelper(addend, augend, 0, [])
}

function baHelper(addend, augend, cin, result) {
  if (addend.length === 0 && augend.length === 0) {
    result.unshift(cin)
    return result.join('')
  } else {
    var a = addend.pop()
    var b = augend.pop()
    var [cout, sum] = fullAdder(a, b, cin)
    result.unshift(sum)
    return baHelper(addend, augend, cout, result)
  }
}

// test:
// 0b10010010 + 0b10101010 = 0b10111111111 (binary)
// 146 + 170 = 316 (decimal)
var result = binaryAdder('10010010', '10101010')
console.log(result)