# Introduction to combinational logic circuits

what are the combinational logic circuits? The combination logic circuit is defined as, the logic circuit which is totally depend on the input, which means that whatever the output is always dependent on the input is known as combination logic circuits.

The example of the combinational circuits are adder, decoder , multiplier , converter and subtractor. In computer circuits, combinational logic is used to compute Boolean algebra on input signals and stored data. The finite time required for practical logical elements to react to changes in their inputs could be a consideration in the design of combinational logic systems.

The three main categories of the combinational circuits are arithmetic or logic function , data transmission and code converter .

First of all, there are two types of logical circuits are:

- Sequential logic circuits
- Combinational logic circuits

So in this we are discussing about the combinational logic circuits. Combinational logic circuits are memoryless circuits whose output at any instant of time is totally depend on the input state as they are determined by “0” and “1” at any instant of time. So if we change the input state then by default the outputs will change as it depends on input that’s why combinational logic circuits have no timing and feedback loop within there design.

All combinational logic circuits can be expressed the by two terms :

Just by OR’ing the AND’ed term or by AND’ing the OR’ing term . through this all combinational circuits can expressed . these terms are also called as sum of products or product of sum.

The logic gates like NAND , NOR , NOT are used to connect or join to form the simple and the difficult logic switching . so, the NAND and NOR are used to design combinational circuits. As these are the universal logic gates. A combinational logic circuits are formed by input variable , logic gate and output variable . so , the input signal transmitted to the logic gate and after process, it generates output . so in this process the input changes into the output by transforming the binary information in to required output information. Though both input and output are binary information . It has n inputs which gives m output . so, for n inputs variable it would be 2 raise to power n possible combination of binary input value.

Usually a combinational circuit have input variables, logic gates and output variables. Logic gates get signals from input and displays output. This circuit processes the given binary information at input and transform it into the requires output. Both input and output are expressed in the form of 0s and 1s logic (i.e. logic-0 and logic-1). The combinational circuit of n-inputs will have an out of m numbers. Input source and output destination is known storage registers. These registers are located either inside the combinational circuits or in an external devices. the register in external circuit is know as external register. These external circuits does not effect the combinational circuits. If they have some effect then the circuit will not remain combinational circuit. It will become a sequential circuit. For n input variables, there are 2n combinations of binary input. But there is only one output for one input combination. Boolean function for output is described in form of n-input variables.

In combinational circuits, an input may have one or two wires. When input has only one wire, it represents variable in normal form or primed form. In this case, we have to use an inverter to get the missing input. When input has two wires, it represents variable in both normal and primed form. So in this case, an inverter is not required.

## Discuss the design procedure of combinational logic circuits

So the to design the combination logic circuits we starts with verbal solving of the problem then end by the truth table or by the Boolean expression .

First of all we will understand the problem which is stated . then we understand about the available inputs then by this we understand about the output . afterwards we will make a symbols which are assigned respectively to the input and the output . so after assigning the symbols we create a truth table by the respective operation for the input . after deriving the truth table we have a simplified Boolean expression through this Boolean expression we draw a logic diagram of the given logic combination circuits .

The first step we will take that we should consider about the input and the output . so we will look about the nature of the input what logic operation should be used for the circuit.

After knowing the nature of logical operation we made a truth table , to solve the logical operation . For the truth table we have two column of the input . 1 and 0 in 2 input are obtained by the 2 raised to n binary combination ,where n is the input variable. where the output column is obtained from stated problem . so the output will be either 1 or 0 by some valid combination while some specification occurs that that at some points the output is not 0 or 1 , so this type of occurrence is known as don’t care conditions . the output function is exact same as the the output function derived in the truth table . Though it is the important that the verbal interpretation should be same as the truth table output function is derived .

After solving all logical operation by the truth table . we gat the Boolean expression which is solved under the circumstances of the logic gates using truth table . so it is a output function or expression . we use it and draw the the required output logic gate diagram using the output expression of Boolean expression . which is very useful for the implementation of the gate for the designer.

Some time it is caused an experience that come to an correct interpretation of the output function . but if sometime, it occurs that the verbal interpretation of the output is not that the same condition as the original output exist , that’s why due to wrong interpretation of the output variable, caused the wrong combinational logic circuit .

However , the output of Boolean expression using truth table can be solved by using different methods like algebraic manipulation, using maps , or the tabular procedure . usually, there are many procedure to calculate the Boolean expression . however in particular there are some limitation and procedure required are used to use the certain the method for solving the respective Boolean expression.

So for the practical designing of the combination logic circuits , we should consider some important points in it . first we should use lesser amount of a gates in the designing because if we use larger amount of gates then the complexity level of the circuit will increase . the second point is that the there should be minimum input entering in the gate . the third one is that there should be minimum time for the signal to propagate in the circuit . the other point is that , there should be minimum amount of interconnection and the last is that the limitation of the capabilities of each of the gate . as these are not attain able simultaneously in practical and it is very important for every constitute for the practical application . so, it is very hard to make an general equation that what constituent are applicable for the simplification . so for the simplification we have to used by the elementary objective that we should find some standard Boolean function we formed so by this we can meet it to some certain criteria to solve it . In practice , the designer are tend to go to the Boolean function to write a list that describes the interconnections between the various logic gates. So due to this the suggested deign is not go to the further than the simplified output Boolean expression ,though the logical diagram of expression describes the implementation of the gate.

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what is the difference between sequential and combinational logic circuits?