Combinational Logic

Combinational Logic Circuits

Unlike Sequential Logic Circuits whose outputs are dependant on both their present inputs and their previous output state giving them some form of Memory.

The outputs of Combinational Logic Circuits are only determined by the logical function of their current input state, logic “0” or logic “1”, at any given instant in time.

The result is that combinational logic circuits have no feedback, and any changes to the signals being applied to their inputs will immediately have an effect at the output. In other words, in a Combinational Logic Circuit, the output is dependant at all times on the combination of its inputs. So if one of its inputs condition changes state, from 0-1 or 1-0, so too will the resulting output as by default combinational logic circuits have “no memory”, “timing” or “feedback loops” within their design.

Combinational Logic

 

Combinational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are “combined” or connected together to produce more complicated switching circuits. These logic gates are the building blocks of combinational logic circuits. An example of a combinational circuit is a decoder, which converts the binary code data present at its input into a number of different output lines, one at a time producing an equivalent decimal code at its output.

Combinational logic circuits can be very simple or very complicated and any combinational circuit can be implemented with only NAND and NOR gates as these are classed as “universal” gates.

The three main ways of specifying the function of a combinational logic circuit are:

• 1. Boolean Algebra – This forms the algebraic expression showing the operation of the logic circuit for each input variable either True or False that results in a logic “1” output.
• 2. Truth Table – A truth table defines the function of a logic gate by providing a concise list that shows all the output states in tabular form for each possible combination of input variable that the gate could encounter.
• 3. Logic Diagram – This is a graphical representation of a logic circuit that shows the wiring and connections of each individual logic gate, represented by a specific graphical symbol, that implements the logic circuit.

and all three of these logic circuit representations are shown below.

 

As combinational logic circuits are made up from individual logic gates only, they can also be considered as “decision making circuits” and combinational logic is about combining logic gates together to process two or more signals in order to produce at least one output signal according to the logical function of each logic gate. Common combinational circuits made up from individual logic gates that carry out a desired application includeMultiplexers, De-multiplexers, Encoders, Decoders, Full and Half Adders etc.

Classification of Combinational Logic

 

One of the most common uses of combinational logic is in Multiplexer and De-multiplexer type circuits. Here, multiple inputs or outputs are connected to a common signal line and logic gates are used to decode an address to select a single data input or output switch.

A multiplexer consist of two separate components, a logic decoder and some solid state switches, but before we can discuss multiplexers, decoders and de-multiplexers in more detail we first need to understand how these devices use these “solid state switches” in their design.

Solid State Switches

Standard TTL logic devices made up from Transistors can only pass signal currents in one direction only making them “uni-directional” devices and poor imitations of conventional electro-mechanical switches or relays. However, some CMOS switching devices made up from FET’s act as near perfect “bi-directional” switches making them ideal for use as solid state switches.

Solid state switches come in a variety of different types and ratings, and there are many different applications for using solid state switches. They can basically be sub-divided into 3 different main groups for switching applications and in this combinational logic section we will only look at the Analogue type of switch but the principal is the same for all types including digital.

Solid State Switch Applications

• Analogue Switches – Used in Data Switching and Communications, Video and Audio Signal Switching, Instrumentation and Process Control Circuits …etc.
• Digital Switches – High Speed Data Transmission, Switching and Signal Routing, Ethernet, LAN’s, USB and Serial Transmissions …etc.
• Power Switches – Power Supplies and General “Standby Power” Switching Applications, Switching of Larger Voltages and Currents …etc.

Analogue Bilateral Switches

Analogue or “Analog” switches are those types that are used to switch data or signal currents when they are in their “ON” state and block them when they are in their “OFF” state. The rapid switching between the “ON” and the “OFF” state is usually controlled by a digital signal applied to the control gate of the switch. An ideal analogue switch has zero resistance when “ON” (or closed), and infinite resistance when “OFF” (or open) and switches with RON values of less than 1Ω are commonly available.

Solid State Analogue Switch

 

By connecting an N-channel MOSFET in parallel with a P-channel MOSFET allows signals to pass in either direction making it a Bi-directional switch and as to whether the N-channel or the P-channel device carries more signal current will depend upon the ratio between the input to the output voltage. The two MOSFET’s are switched “ON” or “OFF” by two internal non-inverting and inverting amplifiers.

Contact Types

Just like mechanical switches, analogue switches come in a variety of forms or contact types, depending on the number of “poles” and “throws” they offer. Thus, terms such as “SPST” (single-pole single throw) and “SPDT” (single-pole double-throw) also apply to solid state analogue switches with “make-before-break” and “break-before-make” configurations available.

Analogue Switch Types

 

Individual analogue switches can be grouped together into standard IC packages to form devices with multiple switching configurations of SPST (single-pole single-throw) and SPDT (single-pole double-throw) as well as multi channel multiplexers.

The most common and simplest analogue switch in a single IC package is the 74HC4066which has 4 independent bi-directional “ON/OFF” Switches within a single package but the most widely used variants of the CMOS analogue switch are those described as “Multi-way Bilateral Switches” otherwise known as the “Multiplexer” and “De-multiplexer” IC´s and these are discussed in the next tutorial.

Combinational Logic Summary

Then to summarise, Combinational Logic Circuits consist of inputs, two or more basic logic gates and outputs. The logic gates are combined in such a way that the output state depends entirely on the input states. Combinational logic circuits have “no memory”, “timing” or “feedback loops”, there operation is instantaneous. A combinational logic circuit performs an operation assigned logically by a Boolean expression or truth table.

Examples of common combinational logic circuits include: half adders, full adders, multiplexers, demultiplexers, encoders and decoders all of which we will look at in the next few tutorials.