About Negabinary

Negabinary means base negative two (-2). That is, the $n$th place value is determined by $(-2)^n$.

Negabinary numbers can be evaluated just like any other base system. For example, we can parse the numbers 101, 110, and 1010 as follows:

Challenge

Given two negabinary integers, output the sum of them in negabinary.

You may take inputs in any format that makes sense. However, the output of the function/program must be in the same format as the input

The following ungolfed example takes in two 0-indexed arrays, with the nth entry being the nth place of each number.

function addNegabinary(first, second) {
    let carry = 0;
    let result = [];

    let place = 0;
    while(place < first.length || place < second.length || carry) {
        let num = (first[place] || 0) + (second[place] || 0) + carry;
        let bit;
        switch (num) {
            case -1: bit = 1; carry = 1; break;
            case 0: bit = 0; carry = 0; break;
            case 1: bit = 1; carry = 0; break;
            case 2: bit = 0; carry = -1; break;
            case 3: bit = 1; carry = -1; break;
        }
        result.push(bit);
        place++;
    }
    return result;
}

Try it online!

Some test cases

1 + 0 = 1
1 + 1 = 110        // 1 + 1 = 2
1 + 110 = 111      // 1 + 2 = 3
10 + 1 = 11        // -2 + 1 = -1
10 + 1011 = 110101 // -2 + -9 = -11

1010101 + 1110100 = 110011001

posted over 3 years ago

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1y ago by trichoplax‭

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