num2fourbit.circom

pragma circom 2.1.4;

template Num2Bits(nBits) {
    signal input x;

    signal output b[nBits];

    for (var i = 0; i < nBits; i++) {
       b[i] <-- x \ (2 ** i) % 2;
    }

    for (var i = 0; i < nBits; i++) {
        b[i] * (b[i] - 1) === 0;
    }

    var accum = 0;
    for (var i = 0; i < nBits; i++) {
        accum += 2 ** i * b[i];
    } 
    accum === x;
}

// input is a field element from [0, 16)
// output four signals b0b1b2b3 representing the binary repr of input
template Num2FourBits () {
    signal input x;

    signal output b0;
    signal output b1;
    signal output b2;
    signal output b3;

    b0 <-- x % 2;
    b1 <-- x \ 2 % 2;
    b2 <-- x \ 4 % 2;
    b3 <-- x \ 8 % 2;


    b0 * (b0 - 1) === 0;
    b1 * (b1 - 1) === 0;
    b2 * (b2 - 1) === 0;
    b3 * (b3 - 1) === 0;
    1*b0 + 2*b1 + 4*b2 + 8*b3 === x;

    // log("x", x);
}

component main { public [ x ] } = Num2Bits(4);

/* INPUT = {
    "x": "11"
} */