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1. Combinational Logic Circuits
Encoders , Decoders and Multiplexer.

2. OBJECTIVES:-
• Construction and verification of Binary to Gray code converter.
• Construction and verification of Gray to binary code converter.
• Construction and verification of two to four line decoder.
• Construction and verification of seven segment decoder.
• Construction and verification of Priority encoder.
• Construction and verification of two to one line multiplexer.
• Construction and verification of four to one line multiplexer.

3. Combinational Circuits:-
• A combinational circuit consists of logic gates whose
output at any time is determined by combining the
values of the applied inputs using logic operations.
• A combinational circuit performs an operation that
can be specified logically by a set of Boolean
expressions.
• Combinational circuit consists of input variables,
output variables, logic gates and interconnections. It
accepts n input signals in binary form and delivers m
output signals in binary form.

4. Code:-
• (a)ASCII:-
American standard code for information interchange is
represented according to the standard. Many applications of
digital computers require handling of data that consists of not
only of numbers but also of the letters of alphabets and
certain characters eg. s, t, c etc. The alphanumeric character
is character set of elements that includes 10 decimal digits 26
letters of alphabet. And number of special characters. The
standard code for the alphanumeric character is ASCII.

5. Gray Codes:-
• In gray codes the bits arranged in such a way that it changes by only one bit
as it sequences from one number to next. In other words each gray code
number differ from the preceding number by a single bit so that
transitional error are minimized.eg
• Decimal Binary Gray code
• 0 0000 0000
• 1 0001 0001
• 2 0010 0011
• 3 0011 0010
• 4 0100 0110
• 5 0101 0111
• 6 0110 0101

6. Gray code conversion

7. Procedure :-
• Binary to Gray code
• Prepare code conversion table for binary to gray code.
• Simplify the Boolean equation using SOP or K map.
• Draw the practical logic diagram according to
simplified equation.
• Verify the circuit.

8. Gray code to Binary
•Prepare code conversion table for gray code to
binary.
•Simplify the Boolean equation using SOP or K
map.
•Draw the practical logic diagram according to
simplified equation.
•Verify the circuit.

9. Decoder:-
• Decoder is a combinational logic circuit that essentially performs the
operation which accepts binary codes and converts it into the active
level representing Decimal, Octal Digits etc.
• The basic function of decoder is to detect the presence of specified
combinations of bits on its inputs and to indicate that presence by
specified output level.
• A decoder has N input lines to handle n bits and from one to 2n
output lines.
• If the n-bit decoded information has unused or don’t care
combinations, the decoder output will have less than 2n outputs.ie we
can say n-to-m line decoders where m≤2

10. Types of Decoder
•One to 2 line decoders.
•Two to 4 line decoders.
•Three To 8 Line Decoder.
•BCD to decimal decoder.
• BCD to Seven segments decoder.

11. One to 2 line decoders.
• The simplest is the 1-to-2 line decoder. The truth table is
• A is the address and D is the dataline. D0 is NOT A and D1 is A. The
circuit looks like

12. Two to 4 line decoders.(truth table)

13. Two to Four Line Decoder

14. larger decoders by combining smaller decoders.
•1-to-2 Decoders with their circuits will
show that both circuits are equivalent.
•In a similar fashion a 3-to-8 line decoder
can be made from a 1-to-2 line decoder
and a 2-to-4 line decoder.
•4-to-16 line decoder can be made from
two 2-to-4 line decoders.

15. larger decoders by combining smaller decoders.

16. Multiplexer
• Multiplexer is the operation performed with digital logic
circuit .
• It allows information to be switched from several lines onto a
single line.
• The selection of a particular line is controlled by a set of
selection lines.
• In digital multiplexer there are 2n Input lines and n selection
lines.
• Multiplexer is also called a data selector.
• It selects one of many inputs and steers the binary
information to the output line.

17. Two to one line Multiplexer

18. The truth table for a 2-to-1 multiplexer

19. Modifying Decoder into Multiplexer

20. 4-to-1 multiplexer circuit

21. 4 to 1 line multiplexer

22. MUX USING NAND

23. Table to verify 4 to 1 line Mux
INPUTS SELECT OUTPUT
I0 I1 I2 I3 S0 S1 F
1 0 0 0 0 0
1 0 0 0 0 1
1 0 0 0 1 0
1 0 0 0 1 1
0 1 0 0 0 0
0 1 0 0 0 1
0 1 0 0 1 0
0 1 0 0 1 1
0 0 1 0 0 0
0 0 1 0 0 1
0 0 1 0 1 0
0 0 1 0 1 1
0 0 0 1 0 0
0 0 0 1 0 1
0 0 0 1 1 0
0 0 0 1 1 1

24. Applications of Multiplexer
• Multiplexer allow the process of transmitting different type of data such as
audio, video at the same time using a single transmission line in
communication .
• In telephone network, multiple audio signals are integrated on a single line
for transmission with the help of multiplexers.
• Multiplexers are used to implement huge amount of memory into the
computer, at the same time reduces the number of copper lines required
to connect the memory to other parts of the computer circuit.
• Multiplexer can be used for the transmission of data signals from the
computer system of a satellite or spacecraft to the ground system using the
GPS (Global Positioning System) satellites.

25. DMULTIPLEXER

26. 1 to 4 DMULTIPLEXER

27. Understanding 1- to-4 Demultiplexer:
• The 1-to-4 demultiplexer has 1 input bit, 2 control bit, and 4 output
bits.
• An example of 1-to-4 demultiplexer is IC 74155.
• The input bit is labelled as Data D.
• This data bit is transmitted to the data bit of the output lines.
• This depends on the value of AB, the control input.
• When AB = 01, the upper second AND gate is enabled while other
AND gates are disabled. Therefore, only data bit D is transmitted to
the output, giving Y1 = Data.

28. Applications of Demultiplexer:
• The main application area of demultiplexer is communication system
where multiplexer are used.
• Demultiplexer are also used for reconstruction of parallel data and
ALU circuits.
• Demultiplexer is used in serial to parallel data converter.

29. Differences between combinational and sequential
logic circuits:-
Combinational
• The logic circuit where the
outputs at any instant of time
are entirely depend upon the
inputs present at that time are
combinational logic circuit.
• Does not have storage capability.
• No other controlling parameter
rather than present input.
• As mentioned earlier o/p
present on any instant of time
Sequential
• The logic circuit where the
outputs depends on inputs as
well as the previous state are
sequential circuit.
• May have storage capability.
• May be dictated by control clock
or enable disable control signal.
• Dependent on specified time
sequence.