$parsers

It is an array of functions to execute. These functions run in order, like a pipeline, every time the control reads a DOM value. The functions are called in array order, the result of each function becomes the input for the next function, and the final return value is sent to the $validators collection.

If the parser returns undefined, it means an error occurred. $validators will not be executed, and ngModel will be set to undefined unless ngModelOptions.allowInvalid is set to true. The parse error is stored in ngModel.$error.parse.

$formatters

It is an array of functions that are executed in the pipeline when ngModel changes. The functions are called in reverse order, and each one passes its value back to the next. The last returned value is used as the DOM value.

In the following image, you can see that parsers are used to transform data from the view to the model, and formatters are used to transform data from the model to the view.