1. Combinational Circuits
Chapter 6
Combinational Circuits

2. Chapter Objectives
Understand the different types of combinational circuits
Understand the different types of encoders and decoders
Understand the concept of parity bits
Understand the concept and applications of magnitude comparator

3. Multiplexer Multiplexer (MUX) is a combinational circuit.
It accepts many inputs and transmits the data over a single output.
It is also known as data selector.
The input line is selected by the set of selection lines.
For n input lines, the number of selection lines will be m, where 2m = n.
Select inputs
Data inputs
Data output
MUX

4. Demultiplexer Demultiplexer (DEMUX) is a combinational circuit.
It accepts one input and transmits the data over multiple outputs.
It is also known as data distributor.
The output line is selected by the set of selection lines.
For n output lines, the number of selection lines will be m, where 2m = n.
Select inputs
Data input
Data outputs
DEMUX

5. Decoder
Decoder is similar to demultiplexer, but it does not contain data input.
It is a logic circuit and converts n-bit input to 2n output lines in such a way that the output line will be activated for only one combination of input lines.
If the number of input and output lines are same, then a decoder acts as a converter to convert the Binary code to Gray code or BCD to Excess-3 code.

6. Decoder (Contd..)
An AND gate can be used as the basic binary decoder because the output of the AND gate is HIGH only when all the inputs are HIGH.
For example, if the input binary number is 1110, then the last bit has to be inverted to make all the inputs HIGH. A B
Y=ABCD C D

7. Decoder (Contd..) Decoders can be classified as:
3-to-8 decoder: It has 3 inputs that are used to select one out of eight outputs and it is also known as 1-of-8 decoder.
4-to-16 decoder: It has 4 inputs that are used to select one out of sixteen outputs and it is also known as 1-of-16 decoder.
BCD-to-decimal decoder: It accepts 4-bit BCD as the input and produces 10 outputs corresponding to each decimal digit.
BCD-to-seven-segment decoder: It is used to display decimal digits from 0 to 9. It accepts decimal digits in BCD and generates the corresponding seven-segment code.

8. Liquid Crystal Display
Liquid Crystal Display (LCD) operates at low voltage AC signal drawing less current.
AC voltage is applied between the 7-segment and the backplane. Both of them act as capacitor and draw less current when AC signal is kept low.
The segments in the display are connected to EX-OR gate with one input connected to 7-segment decoder and the other connected to the signal source.

9. Liquid Crystal Display (Contd..)
If the input of the EX-OR gate is LOW, then the output becomes same with the input provided to the backplane.
If the input of the EX-OR gate is HIGH, then the output becomes 180o out of phase with the input provided to the backplane.

10. Encoders
Encoders convert the input signal to the coded output signal.
They have n input lines out of which only one remains active at a time and m output lines, where m<n. ∙
n inputs
m outputs
Encoder

11. Encoders (Contd..) Types of encoders are:
Octal-to-binary encoder: It performs the inverse of 3-to-8 decoder and has eight input lines. It produces 3-bit output corresponding to the input.
Decimal-to-BCD encoder: It consists of ten input lines for ten decimal digits. It produces 4-bit output representing the BCD value of the input.
Priority encoder: It includes the priority function in which the precedence is given to the input with the highest priority, if they all are HIGH.

12. Parity Bit
Parity bit is an extra bit added to the data, which helps in detecting the presence of error in the data while transmitting it from one location to another.
Types of parity bits are:
Even parity: In even parity, an extra bit is added to the data to make the number of 1’s even.
Odd parity: In odd parity, an extra bit is added to the data to make the number of 1’s odd.
EX-NOR gate is used to generate the parity for the data and EX-OR gate is used to check the parity of the data.

13. Code Converter
Code Converter is used to change the data from one binary code to another.
For example, 7-segment decoder can be considered as a code converter that converts the decimal digits to 7-segment code.
Types of code converter are:
BCD-to-binary code converter
Binary-to-gray code converter
Gray code-to-binary converter

14. Magnitude Comparator
Magnitude Comparator is used to compare the magnitude of two numbers A and B.
It generates one of the following results:
A = B
A < B
A > B
Magnitude
comparator A B
A = B
A < B
A > B

15. Magnitude Comparator (Contd..)
Magnitude comparator uses EX-NOR gate to check whether the digits are equal or not.
It uses AND gate to check whether the binary digit is less or greater than the second number.
Comparators are applied:
As part of address decoding circuitry in computers.
To actuate circuitry for driving physical variable to the reference value.