page_title: Asynchronous circuit
section_title: Multi-rail encoding
hierarchical_section_title: Asynchronous circuit / Communication / Data encoding / Multi-rail encoding
context_page_description: In digital electronics, an asynchronous circuit, or self-timed circuit, is a sequential digital logic circuit which is not governed by a clock circuit or global clock signal. Instead it often uses signals that indicate completion of instructions and operations, specified by simple data transfer protocols. This type of circuit is contrasted with synchronous circuits, in which changes to the signal values in the circuit are triggered by repetitive pulses called a clock signal. Most digital devices today use synchronous circuits. However asynchronous circuits have the potential to be faster, and may also have advantages in lower power consumption, lower electromagnetic interference, and better modularity in large systems. Asynchronous circuits are an active area of research in digital logic design.
context_section_description: Multi-rail encoding uses multiple wires without a one-to-one relationship between bits and wires and a separate acknowledge signal. Data availability is indicated by the transitions themselves on one or more of the data wires (depending on the type of multi-rail encoding) instead of with a request signal as in the bundled-data encoding. This provides the advantage that the data communication is delay-insensitive. Two common multi-rail encodings are one-hot and dual rail. The one-hot (a.k.a. 1-of-n) encoding represents a number in base n with a communication on one of the n wires. The dual-rail encoding uses pairs of wires to represent each bit of the data, hence the name "dual-rail"; one wire in the pair represents the bit value of 0 and the other represents the bit value of 1. For example, a dual-rail encoded two bit number will be represented with two pairs of wires for four wires in total. During a data communication, communications occur on one of each pair of wires to indicate the data's bits. In the general case, an m  n encoding represent data as m words of base n.
  Dual-rail encoding with a four-phase protocol is the most common and is also called three-state encoding, since it has two valid states (10 and 01, after a transition) and a reset state (00). Another common encoding, which leads to a simpler implementation than one-hot, two-phase dual-rail is four-state encoding, or level-encoded dual-rail, and uses a data bit and a parity bit to achieve a two-phase protocol.
caption: Diagram of dual rail and 1-of-4 communications. Top: A sender and receiver are connected by data lines and an acknowledge line. Middle: Timing diagram of the sender communicating the values 0, 1, 2, and then 3 to the receiver with the 1-of-4 encoding. Bottom: Timing diagram of the sender communicating the same values to the receiver with the dual-rail encoding. For this particular data size, the dual rail encoding is the same as a 2x1-of-2 encoding.