combinational circuit-Half Adder ,full Adder

this is a simple presentation on
Half combinational logic circuits .to implement a logic, we use logic circuits. There are two types of logic circuits – combinational logic circuits and sequential logic circuits. To implement a logic, we use logic circuits. There are two types of logic circuits – combinational logic circuits and sequential logic circuits. Combinational logic circuits are time-independent circuits that deploy boolean logic to achieve output. This output depends on the current input and nothing else. Arithmetic logic is necessary for any digital system, as we have seen earlier.To implement a logic, we use logic circuits. There are two types of logic circuits – combinational logic circuits and sequential logic circuits. Combinational logic circuits are time-independent circuits that deploy boolean logic to achieve output. This output depends on the current input and nothing else. Arithmetic logic is necessary for any digital system, as we have seen earlier.To implement a logic, we use logic circuits. There are two types of logic circuits – combinational logic circuits and sequential logic circuits. Combinational logic circuits are time-independent circuits that deploy boolean logic to achieve output. This output depends on the current input and nothing else. Arithmetic logic is necessary for any digital system, as we have seen earlier. are time-independent circuits that deploy boolean logic to achieve output. This output depends on the current input and nothing else. Arithmetic logic is necessary for any digital system, as we have seen earlier.A half adder is an arithmetic combinational logic circuit that adds two 1-bit inputs to give the sum and the carry generated as the output.A half adder is an arithmetic combinational logic circuit that adds two 1-bit inputs to give the sum and the carry generated as the output.The half adder circuit adds two single bits and ignores any carry if generated. Since any addition where a carry is present isn’t complete without adding the carry, the operation is not complete. Hence the circuit is known as a half-adder. Let’s write the truth table using general boolean logic for addition

Full Adder using Half Adder:
Compare the equations for half adder and full adder. The equation for SUM requires just an additional input EXORed with the half adder output. So we add the Y input and the output of the half adder to an EXOR gate. Similarly, for the carry output of the half adder, we need to add Y(A+B) in an OR configuration.
Half Subtractor:
Quite similar to the half adder, a half subtractor subtracts two 1-bit binary numbers to give two outputs, difference and borrow. Since it neglects any borrow inputs and essentially performs half the function of a subtractor, it is known as the half subtractor

Full Subtractor:
A full subtractor accounts for the borrow that a half subtractor neglects. Hence it has three inputs and two outputs. We will write the truth table for the full subtractor based on this info.

1. CHAPTER –7
COMBINATIONAL CIRCUIT

2. What is Combinational Circuits?:
It is logical circuits, the output at any
time depends on the logic levels at the
input at that instantonly.
It does not depend on the past
condition.
A combinational circuit transforms
binary information from the given
output data to the required outputdata.

3. Half Adder:
A half adder is a combinational circuit
adds two binarybits.
Block diagram of half adder is as given
below.
H /A
Inputs
A
B
S
C
sum
carry
Block diagram of HalfAdder

4. Half Adder:
There are two input terminals which are
marked as A and B.
Binary numbers the sum of which has to
be made are appliedhere.
There are two output terminals. One
terminal is for sum and the other is the
carry bitC.
Truth table of half adder is shown
below.

5. Half Adder’ truth table:
Input Output
A BCarrySum
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 0
S=A’B+AB’
C=AB

6. K-MAP for HalfAdder:
1
1
B
A
0
1
0 1
1
B
A
0
1
0 1
From the truth table let us construct
the K-MAP to find Boolean expression
for the sum S and carryC.

7. CarryC=AB
HalfAdderDesign:
A
B
S=A'B+AB'

8. Full Adder:
A full adder is a combinational circuit
that performs the arithmetic sum of
three inputbits.
It consists three inputs and twooutputs.
When we want to add two binary
numbers each having two or more bits
the LSB (Least Significant Bit) can be
added by using a halfadder.
Block diagram of full adder is as given
below:

9. Full Adder Diagram:
F /A
Inputs
S
C
sum
carry
Block diagram of FullAdder
C
i
A
B
In this there are three input terminal. One
output is C
i
which is carry from the previous
stage.
A and B are two input terminals. There are
two output terminals. One is final sum S and
the other is final carryC.

10. Full Adder Diagram:
Input Output
A B C Final
Carry C
Final
Sum
C
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1

11. S=A’BC’+AB’C’+A’B’C+ABC
C=ABC’+A’BC+AB’C+ABC
Full Adder Expression:

12. FullAdderDesign:
ABC
S
C

13. K-MAP for FullAdder:
AB
0
1
1 1
1 1
C
i 00 01 11
K-Map forSum
10
C
i
AB
0
1
0001
1
1 1 1
11
K-Map forCarry
10

14. Full Adder circuit after k map simplification:

15. Full Adder circuit using twohalf adders:
S=A’BC’+AB’C’+A’B’C+ABC
=A’BC’+A’B’C+ABC+ AB’C’
=A’(BC’+B’C)+A(BC+B’C’)
=A’(B(XOR)C)+A(B(XNOR)C)
=A’(B(XOR)C)+A(B(XOR)C)’
=(AXOR(B(XOR)C))

16. Full Adder circuit using twohalf adders:
C=ABC’+A’BC+AB’C+ABC
=AB’C+A’BC+ABC+ABC’
=C(AB’+A’B)+AB(C+C’)
=C(AXORB)+AB

17. Full Adder circuit using twohalf adders:

18. Comparison between Half Adderand
FullAdder
HalfAdder FullAdder
1. It is used for 2bit
addition.
1. It is used forMulti
bitaddition.
2.OneEx-OR/ORgate
andoneANDgateare
used.
2. Two Ex-OR/OR
gates and Multiple
AND gates areused.
3. Output is thesum
of twosignals.
3. Output is thesum
of threesignals.
4. Circuit issimple. 4. Circuit is
complicated.

19. Half Sub tractor:
Binary sub tractor can be made using
half sub tractor. Block diagram is shown
below:
Half
Subtractor
Inputs
A
B
Difference
D
B
Borrow
Block diagram of Half Subtractor

20. Half Sub tractor:
There are two input terminals A and B
bits to be subtracted are appliedhere.
There are two output terminals. One is
for the difference signal and the other is
for borrow signal. Truth table is as given
below:

21. Half Sub tractor’ Truthtable:
Input Output
A B Borrow BDifferenceD
0 0 0 0
0 1 1 1
1 0 0 1
1 1 0 0
D=A’B+AB’
B=A’B

22. Half Sub tractor’ Truthtable:
From the truth table we can write the
sum of product expression for difference
D and borrowB.
Half sub tractor using Ex-OR gate.
D=A’B+AB’
B=A’B
A
B
Borrow
B
Difference
D

23. K-MAP for HalfSubtractor:
1
1
A
B
0
1
0 1
1
B
A
0
1
0 1
D=A'B+AB'
B=A'B

24. Circuit for HalfSub tractor:
A
B
B
Borrow
Difference
D
D=A'B+AB'
B=A'B

25. Full Sub tractor:
Block diagram is shownbelow:
Full
Subtractor
Inputs
B
i
A
B
D
B
Difference
Borrow
Block diagram of Full Subtractor

26. Full Sub tractor:
Therearethreeinputterminalsandtwo
outputterminals.
OneinputisAfromwhichthesecond
inputBhastobesubtracted.Third
inputCwillbesubtractedfrom
resultantoutput.
OneoutputisdifferenceDandthe
otheroutputisborrowB
oheretable
isgivenbelow:

27. Full Sub tractor table:
Input Output
A B C Borrow
B
Difference
D
0 0 0 0 0
0 0 1 1 1
0 1 0 1 1
0 1 1 1 0
1 0 0 0 1
1 0 1 0 0
1 1 0 0 0
1 1 1 1 1

28. FullSubtractor Circuit:
ABC
Difference
D
Borrow
B

29. K-MAP for FullSubtractor:
AB
0
1
1 1
1 1
C
i 00 01 11
K-Map forSub
10
C
i
AB
0
1
0001
1
1 1 1
11
K-Map forBorrow
10

30. Full Sub tractor using two halfsub
tractor:
Block diagram of full sub tractor using
two half sub tractor is shownbelow:
H/S1
Inputs
A
B
D
B
Borrow
Block diagram of Full Sub tractor using two half subtractor
B
i
H/S2
Difference
D

31. Parallel binary adder:
AParallelAdderisadigitalcircuit
capableoffindingthearithmeticsum
oftwobinarynumbersthatisgreater
thanonebitinlengthbyoperatingon
correspondingpairsofbitsinparallel.
Itconsistsoffulladdersconnected
inachainwheretheoutputcarryfrom
eachfulladderisconnectedtothe
carryinputofthenexthigherorderfull
adderinthechain.

32. Parallel binary adder: