pub fn add_binary(a: String, b: String) -> String { // Pad the strings with leading zeroes so they're the same length. let (a, b) = ( format!("{:0>1$}", a, b.len()), format!("{:0>1$}", b, a.len()), ); let mut carry = false; let mut sum = String::new(); // Create reversed iterators for both binary strings. let mut b = b.chars().rev(); for a in a.chars().rev() { // Safe to unwrap since we know both iterators will be the same length. let b = b.next().unwrap(); match (a, b) { ('1', '1') => { // For 1 + 1, if we need to carry it will be 01 + 01 -> 10 + 01 -> 11. // And otherwise it will be 01 + 01 -> 10, and carry next digit. if carry { sum.push('1'); } else { sum.push('0'); carry = true; } } // For 1 + 0 (and associatively 0 + 1), if we need to carry it's the same // as 01 + 01 -> 10. And keep the carry set. // And otherwise it will just be 01 + 00 -> 01. ('1', '0') | ('0', '1') => { if carry { sum.push('0'); } else { sum.push('1'); } } // For 0 + 0, if we need to carry it results in 1 and otherwise 0. ('0', '0') => { if carry { sum.push('1'); carry = false; } else { sum.push('0'); } } _ => unreachable!(), } } // And if the final digits required carrying, add the 1 here at the end. if carry { sum.push('1'); } sum.chars().rev().collect() }