A machine that returns four bits for four bits is called a hex machine.
An initial 2D array of bits is partitioned into square arrays of size 2. Each quartet of bits is transduced into the same number of bits at new quartet positions according to a rule given by 16 base-16 digits. The rules for this transduction are set by the controls at the left. The array is then shifted to perform a similar transduction by the rules defined by the controls at the right side and shifted back.
A byte machine rule is conservative if the number of 1-bits in each rule digit is equal to the number of 1-digits in its Wolfram rule-order digit-position.
Green backgrounds for controls indicate that a particular rule is conservative. You can select identity rules, random rules, conservative rules, or copy rules between the controls on the left and right.