The document discusses digital circuits and their classification into combinational and sequential circuits. It describes combinational circuits as having outputs dependent only on current inputs, with no memory element. Examples provided are adders and subtractors. Specifically, it describes half adders and full adders for binary addition, including their truth tables, K-maps, and logic diagrams. Similarly, half subtractors and full subtractors are described for binary subtraction.

1. Introduction
 Digital circuits are divided into two broad categories..
 Combinational Circuits
 Sequential Circuits
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2. Combinational circuits
 Combinational circuits are the circuits in which output at any instant
of time depends upon the input present at that instant of time.
 There is no memory in combinational circuits.
 Example
 Adder, Subtractor
 Video of Combinational circuit
 Video of Sequential circuit
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3. Adder
 Adder is a Combinational circuit that performs addition of numbers.
 Can be used in ALU of Microprocessor, in calculating address in Microprocessor.
 Types of adders
1. Half adder
2. Full adder
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4. Binary Addition
• 0 + 0 = 00 (Decimal 0)
• 0 + 1 = 01 (Decimal 1)
• 1 + 0 = 01 (Decimal 1)
• 1 + 1 = 10 (Decimal 2)
• Lets assume that A and B are bits to added..
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A B S (Sum) C (Carry)
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1

5. Half Adder
 Logic circuit used for addition of two 1 bit
numbers.
 It has two inputs(A and B) and two outputs(
sum and carry)
 Truth Table
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Inputs Output
A B S C
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1

6. Half Adder cont..
 K-map for Sum
 S = A’B + AB’
= A B
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 K-map for Carrry
 C=AB
 Logic circuit

7. Full Adder
 Half adder has only 2 inputs and there is no provision to add a carry
coming from the lower order bits when multibit addition is
performed.
 Example
 So solution is full adder.
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8. Full Adder cont..
 Block Diagram
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Inputs Outputs
A B Cin S C
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
 Truth Table

9. Full Adder cont..
 K-map for Sum
 Sum=A’B’Cin + A’Bcin’ + AB’Cin’ + ABCin
Sum=A B Cin
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 K-map for Carry
• Carry = Acin +BCin +AB

10. Full Adder
Logic Diagram:
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11. Half Subtractor
 Logic circuit used for subtraction of two 1 bit
numbers.
 It has two inputs(A and B) and two outputs(
Difference and Borrow)
 Where A(minuend), B(Subtrahend)
 Truth Table
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Inputs Output (A-B)
A B D(Difference) Bout(Borrow)
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0

12. Half Subtractor cont..
 K-map for Difference
 D = A’B + AB’
= A B
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 K-map for Borrow
 Bout=A’B
 Logic circuit

13. Full Subtractor
 Problem with Half subtractor
 So we have Full subtractor which is used for
performing multibit subtraction.
 Example:
 Inputs: A(minuend), B(Subtrahend), Bin(Borrow from
previous stage)
 Output: D(Difference), Bout(Borrow)
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14. Full Subtractor cont..
 Block Diagram
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Inputs Outputs
A B Bin D Bout
0 0 0 0 0
0 0 1 1 1
0 1 0 1 1
0 1 1 0 1
1 0 0 1 0
1 0 1 0 0
1 1 0 0 0
1 1 1 1 1
 Truth Table

15. Full Subtractor cont..
 K-map for Difference
 D=A’B’Bin + A’BBin’ +AB’ Bin’ + ABBBin
D=A B Bin
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 K-map for Borrow
• Bout =A’Bin + BBin + A’B