Computer Science Combinational Logic - A Brief Introduction

Combinational Logic – A Brief Introduction

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Logic we typically use in our day to day life – when take a decision, or when do something. Like – If this happen, do that thing, else, go somewhere and do other thing. In Computer Engineering, Logic refers to the functionality of Logic Elements. Such as Logic Gates – AND, NAND, OR, XOR, etc. Therefore, to understand the Combinational Logic or, Logic Circuit, it is important to know very well the functionality of Logic Elements.

For example – An AND Gate gives an output TRUE, only when all of its inputs are TRUE, otherwise FALSE. Similarly an OR gate gives an output TRUE or 1, if any of its input is TRUE. These are the low level logic of computer architecture.

Combinational Logic Or Logic Circuit

Combinational Logic in Digital System is a binary logic (0 or 1) defined by Boolean functions. Or, it is an output logic of Logic Circuit. Logic Circuits we use in Digital System either Sequential or Combinational. A Combinational Logic Circuit consists of an interconnection of Logic Gates. A Logic Circuit performs an operation that can be specified logically by a set of Boolean functions. Outputs at any time of such circuit are determined from only the present combination of inputs.[mathjax]

A block diagram of a combinational circuit is shown in above Fig. The n input binary variables come from an external source. Internal combinational logic circuit produces m output variables and go to an external destination. Each input and output variable exists physically (like – electric voltage) as an analog signal whose values are interpreted to be a binary signal (either ON or OFF). In most practical cases the source and destination are storage registers. If registers are included with the Combinational Gates, then the Combinational Circuit is considered to be a Sequential Circuit.

For n input variables, there are $2^{n}$ possible combinations of the binary inputs. For each possible input combination, there is one possible value for each output variable. Thus, a truth table can list the output values of a logic circuit for each combination of input variables. A combinational Logic circuit also can be described by m Boolean functions, one for each output variable. Each output function is expressed in terms of the n input variables.

Combinational Logic – an Integrated Circuit

There are several combinational circuits that are employed extensively in the design of digital systems. These circuits are available in integrated circuits and are classified as standard components. They perform specific digital functions commonly needed in the design of digital systems. In this section, we will discuss the most important standard combinational Logic circuits, such as adders, subtractors, comparators, decoders, encoders, and multiplexers. These components are available in integrated circuits as medium-scale integration (MSI) circuits. They are also used as standard cells in complex very large scale integrated (VLSI) circuits such as application-specific integrated circuits (ASICs). The standard cell functions are interconnected within the VLSI circuit in the same way that they are used in multiple-IC MSI design.

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