Editing Gray code (section)

=== Cycling through states with minimal effort ===

If a system has to cycle sequentially through all possible combinations of on-off states of some set of controls, and the changes of the controls require non-trivial expense (e.g. time, wear, human work), a Gray code minimizes the number of setting changes to just one change for each combination of states. An example would be testing a piping system for all combinations of settings of its manually operated valves.

A [[balanced Gray code]] can be constructed,<ref name="Bhat-Savage_1996"/> that flips every bit equally often. Since bit-flips are evenly distributed, this is optimal in the following way: balanced Gray codes minimize the maximal count of bit-flips for each digit.

==== Gray code counters and arithmetic ====
[[George R. Stibitz]] utilized a reflected binary code in a binary pulse counting device in 1941 already.<ref name="Stibitz_1941"/><ref name="Winder_1959"/><ref name="Knuth_2014"/>

A typical use of Gray code counters is building a [[FIFO (computing and electronics)|FIFO]] (first-in, first-out) data buffer that has read and write ports that exist in different clock domains. The input and output counters inside such a dual-port FIFO are often stored using Gray code to prevent invalid transient states from being captured when the count crosses clock domains.<ref name="Donohue_2003"/> The updated read and write pointers need to be passed between clock domains when they change, to be able to track FIFO empty and full status in each domain. Each bit of the pointers is sampled non-deterministically for this clock domain transfer. So for each bit, either the old value or the new value is propagated. Therefore, if more than one bit in the multi-bit pointer is changing at the sampling point, a "wrong" binary value (neither new nor old) can be propagated. By guaranteeing only one bit can be changing, Gray codes guarantee that the only possible sampled values are the new or old multi-bit value. Typically Gray codes of power-of-two length are used.

Sometimes digital buses in electronic systems are used to convey quantities that can only increase or decrease by one at a time, for example the output of an event counter which is being passed between clock domains or to a digital-to-analog converter. The advantage of Gray codes in these applications is that differences in the propagation delays of the many wires that represent the bits of the code cannot cause the received value to go through states that are out of the Gray code sequence. This is similar to the advantage of Gray codes in the construction of mechanical encoders, however the source of the Gray code is an electronic counter in this case. The counter itself must count in Gray code, or if the counter runs in binary then the output value from the counter must be reclocked after it has been converted to Gray code, because when a value is converted from binary to Gray code,<ref group="nb" name="NB_Arithmetic_conversion"/> it is possible that differences in the arrival times of the binary data bits into the binary-to-Gray conversion circuit will mean that the code could go briefly through states that are wildly out of sequence. Adding a clocked register after the circuit that converts the count value to Gray code may introduce a clock cycle of latency, so counting directly in Gray code may be advantageous.<ref name="Hulst_1957"/>

To produce the next count value in a Gray-code counter, it is necessary to have some combinational logic that will increment the current count value that is stored. One way to increment a Gray code number is to convert it into ordinary binary code,<ref name="Powell_1968"/> add one to it with a standard binary adder, and then convert the result back to Gray code.<ref name="Mehta-Owens-Irwin_1996"/> Other methods of counting in Gray code are discussed in a report by [[Robert W. Doran]], including taking the output from the first latches of the master-slave flip flops in a binary ripple counter.<ref name="Doran_2007"/>

==== Gray code addressing<span class="anchor" id="Shifted Gray encoding"></span> ====

As the execution of [[program code]] typically causes an instruction memory access pattern of locally consecutive addresses, [[bus encoding]]s using Gray code addressing instead of binary addressing can reduce the number of state changes of the address bits significantly, thereby reducing the [[CPU power consumption]] in some low-power designs.<ref name="Su-Tsui-Despain_1994"/><ref name="Guo-Parameswaran_2010"/>