DIGITAL ELECTRONICS
Unit 4-Combinational circuit
Dr.K.Kalaiselvi
Dept of Computer Science
Kristu Jayanti college
Bangalore

Combinational Logic
 Logic circuits for digital systems may be
combinational or sequential.
 A combinational circuit consists of input variables,
logic gates, and output variables.
2

IMPLEMENTING LOGIC CIRCUIT FROM TRUTH
TABLE

TYPES OF COMBINATIONAL
CIRCUITS
 ARITHMETIC CIRCUITS
HALF/FULL ADDER
HALF/FULL SUBTRACTOR
BINARY PARALLEL ADDER
ADDER-SUBTRACTOR
BCD ADDER
 MAGNITUDE COMPARTOR
 CODE CONVERSION CIRCUITS
 ENCODER
 DECODER
 DATA SELECTION CIRCUITS
MULTIPLEXER
DEMULTIPLEXER
 PARITY GENERATORS/ CHECKERS

HALF ADDER USING NAND

Full adder
Full Adder is the adder which adds three inputs and produces
two outputs. The first two inputs are A and B and the third input
is an input carry as C-IN. The output carry is designated as C-
OUT and the normal output is designated as S which is SUM.
A full adder logic is designed in such a manner that can take
eight inputs together to create a byte-wide adder and cascade
the carry bit from one adder to the another.
Block Diagram

Truth table
Sum = A⊕B⊕CIN
Cout= A’BCin + A’Bcin+ABCin’+ABCin
Cin(A’B+AB’) +AB(Cin+Cin’)
Cin(A’B+AB’) + AB
Cin(A ⊕B) + AB

Full adder using logic gates

Full adder using NAND gates

Half subtractor
Block diagram:
Truth Table:
Expression :
Difference = A XOR B
Borrow = A’B
Half subtractor is used to perform two binary digits subtraction

Half subtractor using NAND
gates

Full subtractor
A full subtractor is a combinational circuit that performs
subtraction of two bits, one is minuend and other is
subtrahend, taking into account borrow of the previous
adjacent lower minuend bit. This circuit has three inputs
and two outputs.
Block Diagram:
Truth Table

Logical expression for difference –
Logical expression for Difference-
D = A’B’Bin + A’BBin’ + AB’Bin’ + ABBin
= Bin(A’B’ + AB) + Bin’(AB’ + A’B)
= Bin( A XNOR B) + Bin’(A XOR B)
= Bin (A XOR B)’ + Bin’(A XOR B)
= Bin XOR (A XOR B) = (A XOR B) XOR Bin

Logical expression for borrow –
Bout = A’B’Bin + A’BBin’ + A’BBin + ABBin
= A’B’Bin +A’BBin’ + A’BBin + A’BBin + A’BBin + ABBin
= A’Bin(B + B’) + A’B(Bin + Bin’) + BBin(A + A’)
= A’Bin + A’B + Bbin
Bout = A’B’Bin + A’BBin’ + A’BBin + ABBin
= Bin(AB + A’B’) + A’B(Bin + Bin’)
= Bin( A XNOR B) + A’B
= Bin (A XOR B)’ + A’B

Full subtractor

4-bit parallel binary adder
 A n bit parallel adder requires n full adders to perform the
operation.

Parallel Addition

4 bit parallel binary adder circuit

Carry methods in parallel adder
o Ripple carry adder
A ripple carry adder is a logic circuit in which the carry-out of
each full adder is the carry in of the succeeding next most
significant full adder. It is called a ripple carry adder because
each carry bit gets rippled into the next stage.
o Carry look-ahead adder
Carry Look –ahead (CLA) adder: speeds up addition process by
eliminating ripple carry delay. This adder anticipates the output
carry of each stage and based on the input bits of each stage ,
produces the output carry by either carry-generation or carry –
propogation.

ADDER-SUBTRACTOR CIRCUIT
A circuit which performs both addition and subtraction.
Sub/add
M=0 for
addition
M=1 for
subtractio
n
For addition: 2nd number is in TRUE form.
For Subtraction: 2nd number is in 2’s complement

Pin diagram for adder-subtractor
circuit

BCD Adder
 BCD adder is an arithmetic unit which performs operations of numbers that
are stored in BCD form.
 has ability to add 4-bit representations of decimal digits.
 BCD adder adds the augend, addend and the carry-in , then produces sum
and carry out
 Constructed using full adders , AND ,OR gates
 Has only 4 augend bits, can have only 10 outputs (0000 to 1001) (0 to 9)
 Sums greater than 9 (1010,1011,1100,1101,1110 and 1111) 6 outputs have
to be corrected.
 The numbers 1010 to 1111 can be avoided by adding the bit pattern 0110 (
decimal 6)

examples
Input : A = 0111 B = 1000
Output : Y = 1 0101
Explanation: We are adding A(=7) and B(=8).
The value of binary sum will be 1111(=15). But, the BCD sum will be 1 0101,
where 1 is 0001 in binary and 5 is 0101 in binary.
Input :
A = 0101 B = 1001
Output :
Y = 1 0100
Explanation: We are adding A(=5) and B(=9).
The value of binary sum will be 1110(=14).
But, the BCD sum will be 1 0100,
where 1 is 0001 in binary and 4 is 0100 in binary.

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.

 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.
 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
1-Bit Magnitude Comparator

Circuit for magnitude comparator
 Try for 2 bit comparator
 Truth table
 Circuit

Code convertor circuits
A code is a set of bits arranged in a unique pattern that
is used to represent specified information.
A code converter is a circuit used to convert one form
of coded information into another coded form
Types:
1. Encoder
2. Decoder

Encoder circuit
It is a logic circuit that performs the encoding function.
Converts information such as a decimal number or an
alphabetic character into some coded form.
Example
Decimal to BCD encoder

An Encoder is a combinational circuit that performs the reverse
operation of Decoder.It has maximum of 2^n input lines and ‘n’
output lines, hence it encodes the information from 2^n inputs into an
n-bit code.
It will produce a binary code equivalent to the input, which is active
High. Therefore, the encoder encodes 2^n input lines with ‘n’ bits.

4 : 2 Encoder
 The 4 to 2 Encoder consists of four inputs Y3, Y2, Y1 & Y0 and
two outputs A1 & A0. At any time, only one of these 4 inputs
can be ‘1’ in order to get the respective binary code at the output.
The figure below shows the logic symbol of 4 to 2 encoder :

The Truth table of 4 to 2 encoder
Logical expression for A1 and A0 :
A1 = Y3 + Y2
A0 = Y3 + Y1

Decimal to BCD Encoder
The decimal to binary encoder usually consists of 10 input
lines and 4 output lines. 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. The figure below shows the logic symbol of
decimal to BCD encoder :

Logical expression for A3, A2, A1 and A0 :
A3 = Y9 + Y8
A2 = Y7 + Y6 + Y5 +Y4
A1 = Y7 + Y6 + Y3 +Y2
A0 = Y9 + Y7 +Y5 +Y3 + Y1

 END