FourBitBinary

pragma circom 2.1.8;

// Create a circuit that takes an array of four signals
// `in`and a signal s and returns is satisfied if `in`
// is the binary representation of `n`. For example:
// 
// Accept:
// 0,  [0,0,0,0]
// 1,  [1,0,0,0]
// 15, [1,1,1,1]
// 
// Reject:
// 0, [3,0,0,0]
// 
// The circuit is unsatisfiable if n > 15

template FourBitBinary() {
    signal input in[4];
    signal input n;

}

component main{public [n]} = FourBitBinary();

Basically, check if the array is the correct binary representation of the input value, n.

Answer

template FourBitBinary() {
    signal input in[4];
    signal input n;

    // constraint all inputs to be 1 or 0
    for (var i = 0; i < 4; i++) {
        // in[i] must be either 1 or 0
        in[i] * (1 - in[i]) === 0;
    }
    
    //    (2^3 * w)   + (2^2 * x)   + (2^1 * y)  + (2^0 * z)
    n === (8 * in[3]) + (4 * in[2]) + (2 * in[1]) + in[0];
}

component main{public [n]} = FourBitBinary();