Source

File: wp-includes/widgets/class-wp-widget-categories.php

public function update( $new_instance, $old_instance ) {
		$instance                 = $old_instance;
		$instance['title']        = sanitize_text_field( $new_instance['title'] );
		$instance['count']        = ! empty( $new_instance['count'] ) ? 1 : 0;
		$instance['hierarchical'] = ! empty( $new_instance['hierarchical'] ) ? 1 : 0;
		$instance['dropdown']     = ! empty( $new_instance['dropdown'] ) ? 1 : 0;

		return $instance;
	}