binary-to-decimal.js

// Explanation:
// In decimal system: 142 = 100 + 40 + 2 = (1 * 10^2) + (4 * 10^1) + (2 * 10^0) = 142
// In binary system: 101 = (1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 4 + 0 + 1 = 5

function binaryToDecimal(v) {
  const first = v[0];
  const exp = v.length - 1;
  const val = parseInt(first) * (2 ** exp);
  if (v.length === 0) {
    return NaN;
  } else if (v.length === 1) {
    return val;
  } else {
    const rest = v.slice(1);
    return val + binaryToDecimal(rest);
  }
}

binaryToDecimal("100"); // 4
binaryToDecimal([1, 0, 0]); // 4
binaryToDecimal("100001"); // 33
binaryToDecimal("11111111"); // 255

decimal-to-binary.js

// Rough explanation:
// If v is 0, then return "0".
// 1. Modulo divide v by 2. Collect this first remainder as the last digit of the final result - binary equivalent of v.
// 2. Modulo divide resulting quotient by 2. Collect the remainder as the nth from the last digit of the final result.
// 3. Repeat step 2 until quotient is 0.
// 4. The collected remainders is the binary equivalent of v.

// Example: v = 9
// 9 mod 2 = 4 (quotient), 1 (remainder). result: "1"
// 4 mod 2 = 2 (quotient), 0 (remainder). result: "01"
// 2 mod 2 = 1 (quotient), 0 (remainder). result: "001"
// 2 mod 1 = 0 (quotient), 1 (remainder). result: "1001"
// Final Result: "1001"

function decimalToUnsignedBinary(v) {
  const absV = Math.abs(v);
  if (absV === 0) {
    return "0";
  } else if (absV === 1) {
    return "1";
  } else {
    const quotient = Math.floor(absV / 2);
    const remainder = absV % 2;
    return decimalToUnsignedBinary(quotient) + remainder;
  }
}

decimalToUnsignedBinary(0); // => "0"
decimalToUnsignedBinary(1); // => "1"
decimalToUnsignedBinary(10); // => "1010"
decimalToUnsignedBinary(33); // => "100001"
decimalToUnsignedBinary(-33); // => "100001"