Lesson 7: Combinational Logic Circuits

Combinational Logic Circuit

• Consists of logic gates whose outputs at any time are determined directly from the present combination of inputs without regard to previous inputs.

• It does not use any memory.

• It has no storage or clock elements

• Built using logic gates

• Perform data processing operation such as arithmetic and logical function

Characteristics of Combinational Circuits:

Block Diagram of Combinational Ckt:

Logic Function

It is a Boolean expression that defines the output of a circuit with a given set of inputs.

Truth Table

_________ defines the output of a circuit in tabular form for all possible combinations of inputs.

Logic Diagram

_________ is a graphical representation of a circuit showing the connections of each logic gate.

• Adders

• Comparators

• Encoders

• Decoders

• Multiplexers

• Demultiplexers, and

• Code converters (such as binary and BCD).

Common combinational logic circuits have specific applications such as:

• Half Adder

• Full Adder

• Half Subtracter

• Full Subtracter

• Parallel Adder

• BCD Adder

• Magnitude Comparator

• Decoder

• BCD to Decimal Decoder

• Encoder

• Multiplexer

• Demultiplexer

Combinational Logic Circuits Examples:

MEMORIZE IT!!

Half Adder

A _________ adds two single-bit binary numbers (A and B).

Block Diagram of Half Adder:

Half Adder Ckt:

Full adder

• A _________ is simply a half adder that takes in a carry bit from another section

• It is usually a single stage in a cascade of adders used to add large numbers.

Full Adder Block Diagram:

Full Adder Expression:

Full Adder Ckt:

Half Subracter

It subtracts 2 bits mathematically.

Half Subracter Ckt:

Full Subracter

It subtracts 3 bits mathematically.

Full Subracter Ckt:

Binary Parallel Adder

• A _________ is a digital circuit that performs binary addition on two binary numbers simultaneously (in parallel) — meaning that all bits are added at the same time, not one after another.

Look-Ahead Carry Generation (Carry Look-Ahead Adder or CLA)

• It is a fast binary addition technique used to overcome the delay problem of ripple carry adders (like the binary parallel adder).

• It is a method of determining carry outputs directly from the input bits, without waiting for carry propagation from the previous adder stages.

4-Bits Full Adder with Look Ahead Generator Ckt:

BCD Adder (Binary Coded Decimal Adder)

A _________ is a digitalcircuit that adds two decimal numbers represented in BCD (Binary-Coded Decimal) form.

Magnitude Comparator

A _________ is a combinational logic circuit that compares two binary numbers (A and B) and determines their relative magnitude,

BCD-to-Decimal Decoder

A _________ is a combinational logic circuit that converts a 4-bit BCD (Binary-Coded Decimal) input into one of ten active outputs, corresponding to the decimal digits 0 through 9.

Decoder

• A _____ is a combinational logic circuit that converts binary inputs into a unique, active output line.

• An n-bit binary input into 2n possible outputs, with only one output active (HIGH or LOW) at a time.

Decimal-to-BCD Decoder

A _________ (more precisely, a BCD-to-Decimal Decoder) is a combinational logic circuit that converts a BCD input into its corresponding decimal output.

Decimal-to-BCD Decoder Ckt:

Combinational Logic Implementation

• Any Boolean function can be expressed in sum of minterms.

• Use a decoder to generate the minterms and an external OR gate to form the sum.

Encoder

An _____ is a combinational logic circuit that converts active input signals into a coded binary output.

• 4 to 2 Encoder

• 8 to 3 Encoder (Octal Encoder)

• Decimal to BCD Encoder

Types of Encoders:

4 to 2 Encoder

It is a type of encoder which has 4 (2²) input lines and 2 output lines. It produces an output code (i.e., convert input information in a 2-bit format) depending on the combination of input lines.

Octal to binary encoder

The _________ is a type of encoder that converts an octal code into binary code. It accepts 8 input lines and produces a 3-bit output depending on the combination of input lines.

8 to 3 Encoder.

Octal to Binary Encoder also known as?

8 to 3 Encoder Ckt: