> For the complete documentation index, see [llms.txt](https://calnix.gitbook.io/zk-notes/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://calnix.gitbook.io/zk-notes/zk-puzzles-rareskills/multiand.md).

# MultiAND

```solidity
pragma circom 2.1.8;

// Create a circuit that takes an array of signals `in` and
// returns 1 if all of the signals are 1. If any of the
// signals are 0 return 0. If any of the signals are not
// 0 or 1 the circuit should not be satisfiable.

template MultiAND(n) {
    signal input in[n];
    signal output out;

}

component main = MultiAND(4);
```

### Answer

```solidity
template MultiAND(n) {
    signal input in[n];
    signal output out;

    // constraint all inputs to be 1 or 0
    for (var i = 0; i < n; i++) {
        // in[i] must be either 1 or 0
        in[i] * (1 - in[i]) === 0;
    }

    // multiply inputs 
    signal s[n];

    s[0] <== in[0];
    for(var i = 1; i < n; i++){
        s[i] <== s[i - 1] * in[i];
    }
  
    // constraint out value to be RHS
    out <== s[n-1];
    
}

component main = MultiAND(4);
```

If all the values can only be 1 or 0, then when multiplying them together, we should only get 1 or 0 as output values.&#x20;

1. &#x20;constraint input values to be 1 or 0&#x20;
2. multiply. if all are 1, output is 1. if there is at least a single zero term, output is zero.

### Alternative Solution: Non-general

```solidity
template Mul() {
    signal input in[2];
    signal output out;

    out <== in[0] * in[1];
}

template MultiAND(n) {
    signal input in[n];
    signal output out;

    // constraint all inputs to be 1 or 0
    for (var i = 0; i < n; i++) {
        // in[i] must be either 1 or 0
        in[i] * (1 - in[i]) === 0;
    }

    // multiply them together 
    signal a;
    signal b;
    // declare anon component
    a <== Mul()([in[0], in[1]]);
    b <== a * in[2];

    // constraint out value to be RHS
    out <== b * in[3];
    
}
```

* the solution

### Under-constrained example

<figure><img src="https://1983523492-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F0nwEx8a60yETwfNYnenT%2Fuploads%2FBaumOpgwrrNqhkNeW1yg%2Fimage.png?alt=media&amp;token=b0d6e1f4-0d51-45be-b3c0-23f7b54b83ed" alt=""><figcaption></figcaption></figure>

* out is not constrained.
* this is under constrained although the tests clear