07-12-2012, 06:20 PM
Combinational Logic Circuits
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INTRODUCTION
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 Circuitsare only determined by the logical function of their current input state, logic "0" or logic "1", at any given instant in time as they 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 and if one of its inputs condition changes state so does the output as combinational circuits have "no memory", "timing" or "feedback loops".
Combinational Logic Circuits
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:
• Truth Table Truth tables provide a concise list that shows the output values in tabular form for each possible combination of input variables.
• Boolean Algebra Forms an output expression for each input variable that represents a logic "1"
• Logic Diagram Shows the wiring and connections of each individual logic gate that implements the circuit.
and all three are shown below.
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.
The Binary Adder
Another common and very useful combinational logic circuit which can be constructed using just a few basic logic gates and adds together binary numbers is the Binary Adder circuit. The Binary Adder is made up from standard AND and Ex-OR gates and allow us to "add" together single bit binary numbers, a and b to produce two outputs, the SUM of the addition and a CARRY called the Carry-out, (Cout ) bit. One of the main uses for the Binary Adder is in arithmetic and counting circuits.
Binary Addition
Binary Addition follows the same basic rules as for the denary addition above except in binary there are only two digits and the largest digit is "1", so any "SUM" greater than 1 will result in a "CARRY". This carry 1 is passed over to the next column for addition and so on. Consider the single bit addition below.
The Multiplexer
A data selector, more commonly called a Multiplexer, shortened to "Mux" or "MPX", are combinational logic switching devices that operate like a very fast acting multiple position rotary switch. They connect or control, multiple input lines called "channels" consisting of either 2, 4, 8 or 16 individual inputs, one at a time to an output. Then the job of a multiplexer is to allow multiple signals to share a single common output. For example, a single 8-channel multiplexer would connect one of its eight inputs to the single data output. Multiplexers are used as one method of reducing the number of logic gates required in a circuit or when a single data line is required to carry two or more different digital signals.
Digital Multiplexers are constructed from individual analogue switches encased in a single IC package as opposed to the "mechanical" type selectors such as normal conventional switches and relays. Generally, multiplexers have an even number of data inputs, usually an even power of two, n2 , a number of "control" inputs that correspond with the number of data inputs and according to the binary condition of these control inputs, the appropriate data input is connected directly to the output. An example of a Multiplexer configuration is shown below.
The Digital Encoder
Unlike a multiplexer that selects one individual data input line and then sends that data to a single output line or switch, a Digital Encoder more commonly called a Binary Encoder takes ALL its data inputs one at a time and then converts them into a single encoded output. So we can say that a binary encoder, is a multi-input combinational logic circuit that converts the logic level "1" data at its inputs into an equivalent binary code at its output. Generally, digital encoders produce outputs of 2-bit, 3-bit or 4-bit codes depending upon the number of data input lines. An "n-bit" binary encoder has 2n input lines andn-bit output lines with common types that include 4-to-2, 8-to-3 and 16-to-4 line configurations. The output lines of a digital encoder generate the binary equivalent of the input line whose value is equal to "1" and are available to encode either a decimal or hexadecimal input pattern to typically a binary or B.C.D. output code.