- Combinational circuits consist of logic gates whose outputs depend only on the present inputs. They have no memory. - A half adder is a basic combinational circuit that adds two 1-bit numbers and produces a sum and carry output. A full adder adds three 1-bit numbers. - Other common combinational circuits described in the document include half and full subtractors, magnitude comparators, encoders, decoders, multiplexers, and demultiplexers. Each has a specific function and truth table defining its input-output behavior.

4. 4
• Combinational circuits consists of logic gates
whose outputs depends on the present inputs
• They have no memory element .
• It consists of input variables , logic gates &
output variables .
Introduction

6. Half adder is a combinational logic circuit which add two 1-bit data (A,B) and
produces the outputs as sum (s) and carry (C) It is the basic building block for
addition of two single bit numbers. This circuit has two outputs carry and sum.
Definition
Block Diagram Truth table
Expression:
Sum, S= A⊕B
Carry, C= AB

7. Circuit Diagram
Working
• When A= 0, B=0 then S=0 C=0
• When A= 0, B=1 then S=1 C=0
• When A= 1, B=0 then S=1 C=0
• When A= 1, B=1 then S=0 C=1

8. Full adder is developed to overcome the drawback of Half Adder circuit. It is a
combinational circuit which adds three 1-bit data (A, B, Cin) to produce the
output as sum(s) and carry(Co).
Definition
Block Diagram Truth table
Expression:
Sum, S= (A ⊕ B) ⊕ Cin
Carry, Co= A.B + Cin (A ⊕ B)

9. Circuit Diagram
Working
• When A= 0, B=0, C=0 then S=0 Co=0
• When A= 0, B=0, C=1 then S=1 Co=0
• When A= 0, B=1, C=0 then S=1 Co=0
• When A= 0, B=1, C=1 then S=0 Co=1
• When A= 1, B=0, C=0 then S=1 Co=0
• When A= 1, B=0, C=1 then S=0 Co=1
• When A= 1, B=1, C=0 then S=0 Co=1
• When A= 1, B=1, C=1 then S=1 Co=1
Sum, S= (A ⊕ B) ⊕ Cin
Carry, Co= A.B + Cin (A ⊕ B)

10. IT IS A COBINATIONAL CIRCUIT WHICH SUBTRACTS THE INPUT DATA AND PRODUCE THE
OUTPUT AS DIFFERENCE AND BORROW

11. Half-subtractor is a combinational circuit which is used to subtract two 1-bit
data (A, B) to give the output as Difference (Diff) and a Borrow (Br)
Definition
Block Diagram Truth table
Expression:
Difference Diff= A⊕B
Borrow Br= 𝑨B

12. Circuit Diagram
Working
• When A= 0, B=0 then Diff=0 Br=0
• When A= 0, B=1 then Diff=1 Br=1
• When A= 1, B=0 then Diff=1 Br=0
• When A= 1, B=1 then Diff=0 Br=0

13. Full subtractor is a combinational circuit which subtracts three 1-bit data (A, B,
C) to produce the output as Difference (Diff) and Borrow (Br).
Definition
Block Diagram
Truth table
Expression:

14. Circuit Diagram
Working
• When A= 0, B=0, C=0 then Diff=0 Br=0
• When A= 0, B=0, C=1 then Diff=1 Br=1
• When A= 0, B=1, C=0 then Diff=1 Br=1
• When A= 0, B=1, C=1 then Diff=0 Br=1
• When A= 1, B=0, C=0 then Diff=1 Br=0
• When A= 1, B=0, C=1 then Diff=0 Br=0
• When A= 1, B=1, C=0 then Diff=0 Br=0
• When A= 1, B=1, C=1 then Diff=1 Br=1

15. Full Subtractor using NAND gate

17. Magnitude Comparator
A magnitude digital Comparator is a combinational circuit that compares two
digital or binary numbers in order to find out whether one binary number is
equal, less than or greater than the other binary number.
We logically design a circuit for which we will have two inputs one for A and
other for B and have three output terminals, one for A > B condition, one for
A = B condition and one for A < B condition.

18. 1-Bit Magnitude Comparator
• A comparator used to compare two bits is called a single bit comparator. It
consists of two inputs each for two single bit numbers and three outputs
to generate less than, equal to and greater than between two binary
numbers.
• A Comparator is a combinational circuit which compares two inputs (A , B)
and gives the output as either A<B or A=B or A>B
• The truth table for a 1-bit comparator is given below:
From the above truth table logical expressions for each output can be expressed as
follows:
A>B: AB'
A<B: A'B
A=B: A'B' + AB

19. A 2-bit comparator is a combinational circuit that compares two 2-bit numbers(A &
B) and produce the output as either A<B or A=B or A>B.
The figure shows the block diagram of a two-bit comparator which has four inputs
and three outputs
Definition
Block Diagram
The first number A is designated as A = A1A0 and the second number is designated
as B = B1B0.
This comparator produces three outputs as A>B, Or A = B Or A<B.

21. Truth table
Expression:

22. Circuit Diagram

23. Encoder is a combinational circuit that converts the data from understandable
format to coded format.
Definition
Block Diagram
• A binary encoder has 2n input lines
and n output lines, hence it encodes
the information from 2n inputs into
an n-bit code.
• Any 1 input line will be activated at
time
• Based on the number of inputs
encoders are classified as 4:2, 8:3,
16:4, decimal to BCD encoder.

24. This type of encoder usually consists of 10 input lines (D0 to D9) and 4 output
lines (Y3 , y2, y1, y0).
Each input line corresponds to the each decimal digit and 4 outputs correspond
to the BCD code.
This encoder accepts the decoded decimal data as an input and encodes it to the
BCD output which is available on the output lines
Definition
Block Diagram

25. Circuit Diagram
Truth table
Expression:
Y3 = D8 + D9
Y2 = D4 + D5 + D6 + D7
Y1 = D2 + D3 + D6 + D7
Y0 = D1 + D3 + D5 + D7 + D9

26. The Priority Encoder solves the problem that only one input should be high at a
time by allocating a priority level to each input. The priority encoders output
corresponds to the currently active input which has the highest priority. So when
an input with a higher priority is present, all other inputs with a lower priority
will be ignored.
Definition
Truth table
Here D9 has the highest priority. For example if D7 & D5 are high at a time, then this
encoder will produce the output for D as 0111 because D has more priority than D

27. Decoder is a combinational logic circuit that converts coded input to
understandable outputs provided both of these are different from one another.
The name decoder means translating of coded information from one format into
another
Definition
Block Diagram
• A binary decoder is a multi-input, multi-
output combinational circuit that converts a
binary code of n input lines into a one out of
2n output code.
• These are used when there is need to
activate exactly one of 2n output based on
an n-bit input value.
• Based on the number of inputs & outputs
decoders are classified as 2:4, 3:8, 4:16,
BCD to decimal decoder.
• No of outputs = (𝟐)𝑵𝒐 𝒐𝒇 𝒊𝒏𝒑𝒖𝒕𝒔

28. It is a combinational circuit which converts the data from binary format to
decoded format. It has 2 inputs (A, B) and 4 outputs (Y3, Y2, Y1, Y0). Any one of
the output will be high at a time based on the input combination
Definition
Block Diagram
Inputs outputs
A B Y3 Y2 Y1 Y0
0 0 0 0 0 1
0 1 0 0 1 0
1 0 0 1 0 0
1 1 1 0 0 0
Truth table
Working
When A = 0 and B = 1, the output Y1 will be active and when A = 1 and B = 0, then
the output Y2 will be active. When both the inputs are high, then the output Y3
will be high. If the enable bit is zero then all the outputs will be set to zero. This
relationship between the inputs and outputs are illustrated in the truth table

29. Expression: Circuit Diagram

30. In a 3-to-8 decoder, three inputs are decoded into eight outputs. It has three
inputs as A, B, and C and eight output from Y0 through Y7. Based on the
combinations of the three inputs, only one of the eight outputs is selected.
Definition
Block Diagram Truth table
Working
The working of 3:8 decoder is as shown in the truth table. The decoded output
depends on the input combinations A, B and C. Suppose if A = B=1 and C= 0, then
the output Y6 is 1 and all other outputs are zero.

31. Expression: Circuit Diagram

32. The BCD-to-decimal decoder is a combinational circuit that converts each BCD
code to its decimal equivalent. The decoded output depends on the input
combinations A, B, C and D.
Definition
Truth table
Working
The working of BCD to decimal decoder is as shown in the truth table. The
decoded output depends on the input combinations A, B, C and D.
Suppose if A =0, B=1, C= 0, D=1 then the output D5 is 1 and all other outputs are
zero. The working of 3:8 decoder is as shown in the truth table.
BCD inputs Decimal Outputs
A B C D D9 D8 D7 D6 D5 D4 D3 D2 D1 D0
0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 1 0 0 0 0 0 0 0 0 1 0
0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 0 1 1 0 0 0 0 0 0 1 0 0 0
0 1 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 0 0 0 0 1 0 0 0 0 0
0 1 1 0 0 0 0 1 0 0 0 0 0 0
0 1 1 1 0 0 1 0 0 0 0 0 0 0
1 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 0
Block Diagram

33. Expression: Circuit Diagram

34. Definition
A BCD to 7 segment decoder is a combinational circuit which is used to convert
a binary or BCD (Binary Coded Decimal) number to the corresponding decimal
number (7-segment display) .
Block Diagram

35. Circuit Diagram Truth table

36. Definition
A 4-to-1 multiplexer consists four data input lines as D0 to D3, two select lines
as S0 and S1 and a single output line Y. The select lines S1 and S2 select one of
the four input lines to connect the output line. The particular input combination
on select lines selects one of input (D0 through D3) to the output
Block Diagram Truth Table
From the above truth table, we can write the output expressions as

37. Circuit:

38. Definition
A 1-to-4 De multiplexer is a combinational circuit that sends the data (D) from
input to any one of 4 outputs (Y0 Y1 Y2 Y3) depending upon the 2 select lines (S1
S0). The figure shows the block diagram of a 1-to-4 Demultiplexer
Block Diagram

39. From the above truth table, we can write the output expressions as
Truth Table

40. Circuit: