# 6 Jaw-dropping Applications of Combinational logic Design

Hello everyone, Hope you all are doing good in your lives. Consequently, The topic for today is Applications of combinational logic design. Firstly before starting with the main topic let’s just have an overview that what are we gonna see further down below. We are certainly going to focus on devices like Multiplex, Demultiplex, comparator, adder, converters, decoders and etc.

**Table of Contents**hide

## What is a Combinational Logic Design?

Certainly in these circuits, the output at any instant of time depends on the input at that instant to time only. However, this means that there is no memory present (for storing previous state value). These circuits generally have p inputs and q outputs. Besides they also do not have feedback and timing.

these functions are specified in terms of logic variables. The number assumed by the logic function and variable are usually express in binary form(i.e. 0 and 1).

### Advantages of Combinational logic design

- Significantly reduces the IC package density which in turn reduces the cost.
- Simple in design because it consist of simple gates.
- Reliability increases because of decrease in external connections.

Thus if the user wants to make use of the circuits in the most useful manner then he/she should be aware of these advantages and limitations. Now, let’s start with the study of various devices which work on this circuitry.

## Combinational logic design as a Multiplexer

**Definition:-** It is a special combinational circuit design that gates one out of many inputs to a single output.

However, it is the most widely used logic design in digital circuits. Because of its large use, it is been producing as MSI IC and is available in various sizes like 2:1, 4:1, 8:1, and 16:1.

Whereas in a multiplexer the input which is selected is on the basis of the number of select lines available. The block diagram henceforth shows the diagram of a multiplex with N input lines and one output line. Certainly for selecting one out of the n inputs for connection to the output. a set of m select inputs are require,

where; 2^{m} = n

Depending on the available code at the input one out of n input lines is select and then, given to the output. Generally, it also consists of a enable pin that helps in connection and is usually active-low. Which means that it operates at a low level.

Whereas output Y is ;

Y = (S_{1}S_{2}I_{o} + S_{1}S_{o}I_{1} + S_{1}S_{o}I_{2} + S_{1}S_{o}I_{3})*G

However, the Truth Table is;

Enable Input | S1 | S2 | Output |

0 | o | 0 | I0 |

0 | o | 1 | I1 |

o | 1 | 0 | I2 |

0 | 1 | 1 | I3 |

1 | X | X | 0 |

Certainly for using multiplexer a logic element either the truth table or the canonical form of logic expression must be present. Available multiplexer IC’s are 74157, 74158, 74153, 74352, 74150.

Consequently implementing a boolean function using 8:1 multiplexer;

F(A,B,C,D) = Σ(1,3,4,11,12,13,14,15)

## Combinational logic design as a DEMULTIPLEXER

However, the demultiplexer performs the exact opposite task of the multiplexer. It accepts a single input and distributes it into several outputs. the figure below gives the block diagram of a demultiplexer. Generally, the code present at the input determines to which output the data input should be transmitted.

Besides here the number of output lines is given by n and select line by m where;

n = 2^{m}

The data input will appear on the output line selected by the select input. For instance, if the decimal equivalent of select input is 5 then data will appear on the D5 output line. Meanwhile, this circuit can also be used as a binary to the decimal decoder with binary value applied to the select input lines and the output will be available at the corresponding output line. Generally, the data input line to be always connected to logic 1. Likewise, a multiplexer is also available as an MSI IC and can be easier for the design of combinational circuits.

These devices are certainly available as 2-line-to-4-line, 3-line-to-8-line, and 4-line-to-16-line decoders. Certainly, the output of most of these devices is active low. Summing up the available IC’s are 74139, 74155, 74156, 74138 and etc.

consequently, represent a full adder with a demultiplexer

S(X,Y,Z) = S m(1,2,4,7) & C(X,Y,Z) = S m(3,5,6,7)

## BCD Adder

The 4-bit binary adder IC (7483) is used to perform the addition of BCD numbers. however here if the four-bit sum output is not a valid BCD digit, or if a carry C3 is obtained, then the addition of decimal 6 is to be done with the result available. However, numbers several digits long can be added by cascading BCD Adders together by connecting the carry-out of a stage to the carry-in of the next.

Certainly, BCD Adders which can perform addition up to 6 decimal value

On the other hand BCD Adders can perform addition above 6 decimal value.

## Combinational logic design as a ALU

Certainly, ALU stands for an arithmetic logic unit. it is one of the most popular and widely use combinational logic designs. However, the main function of an ALU is to perform arithmetic as well as logical operations. It is the heart of a microprocessor or a microcontroller. Meanwhile, the diagram given below is the block representation of an ALU;

However, the main function of various input, output, and select lines are mention below.

- A nd B :- 4-bit binary data input
- Cn :- Carry Input
- F = 4- bit binary data input

Similar to demultiplexer the 74181 can also be cascaded by connecting the carryout of one stage to the carry-in of the next stage.

## Combinational logic design as a Digital Comparator

A digital comparator is a combinational logic device that generally takes two inputs in the binary form and compares them that are equal, greater than, or smaller then. The comparator can also be designed for comparing multibit numbers. The figure below shows the block diagram of a digital comparator.

However, it usually receives two n -bit numbers A and B as inputs, and the outputs are A>B, A<B, A=B. depending on the consequent magnitude of the two magnitudes of the number, any one of the outputs will be high. Meanwhile, the reader is advise to simplify the expression for outputs using the k-map and design the circuit using gates. However, 4-bit comparator are available as MSI IC’s which straight compare the binary and natural BCD codes. Likewise others can also be cascaded.

4 bit digital comparator

8 Bit Digital Comparator

## Parity Generaters

The concept of parity, wherein an additional bit known as the parity-bit is added to a binary word to make the number of 1’s, in the new word formed. The circuit for generation parity bits and also for checking the parity of a given word can be designed using gates. Because of its wide use, an 8-bit parity generator/checker circuit has been designed and is available as an MSI IC chip(74180).

Accordingly the block diagram of 74180 in which there are eight parity input A through H and two cascading inputs. Besides, there are two outputs Σ Even and Σ Odd.

Besides truth table is;

Parity of inputs A through H | Cascading Input EVEN ODD | Output EVEN ODD |

Even | 1 0 | 1 0 |

Odd | 1 0 | 0 1 |

Even | 0 1 | 0 1 |

Odd | 0 1 | 1 0 |

X | 1 0 | 0 0 |

X | 0 0 | 1 1 |

## Code Converter

There is a wide variety of binary code uses in a digital system. for instance some of these codes are binary coded decimal, excess 3, gray code octal hexadecimal, etc. Often, it is require to convert from one form to another. For example, the input to a digital system may be in natural BCD and the output may be 7-segment LEDs. The digital system used may be capable of processing the data in a straight binary format. Therefore, the data has to be converted from BCD to binary at the output.

The BCD output has to be converted to a 7-segment code before it is use to drive the LEDs. Similarly, octal and hexadecimal codes are widely used in a microprocessor and digital computer as input and outputs. The various converters can be design using gates, multiplexers,s, or demultiplexers. However, there are some MSI ICs available for performing these conversions and are extremely useful in the designing of a digital system

## Conclusion

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