UNIT I - COMBINATIONAL LOGIC
Combinational Circuits – Karnaugh Map – Analysis and Design Procedures – Binary Adder –
Subtractor – Decimal Adder – Magnitude Comparator – Decoder – Encoder – Multiplexers –
Demultiplexers.
Logic Gates
o The logic gates are the main structural part of a digital system.
o Logic Gates are a block of hardware that produces signals of binary 1 or 0 when input logic requirements
are satisfied.
o Each gate has a distinct graphic symbol, and its operation can be described by means of algebraic
expressions.
o The seven basic logic gates include: AND, OR, XOR, NOT, NAND, NOR, and XNOR.
o The relationship between the input-output binary variables for each gate can be represented in tabular
form by a truth table.
o Each gate has one or two binary input variables designated by A and B and one binary output variable
designated by x.
AND GATE:
The AND gate is an electronic circuit which gives a high output only if all its inputs are high. The AND
operation is represented by a dot (.) sign.
OR GATE:
The OR gate is an electronic circuit which gives a high output if one or more of its inputs are high. The
operation performed by an OR gate is represented by a plus (+) sign.
NOT GATE:
The NOT gate is an electronic circuit which produces an inverted version of the input at its output. It
is also known as an Inverter.
, NAND GATE:
The NOT-AND (NAND) gate which is equal to an AND gate followed by a NOT gate. The NAND
gate gives a high output if any of the inputs are low. The NAND gate is represented by a AND gate
with a small circle on the output. The small circle represents inversion.
NOR GATE:
The NOT-OR (NOR) gate which is equal to an OR gate followed by a NOT gate. The NOR gate gives
a low output if any of the inputs are high. The NOR gate is represented by an OR gate with a small
circle on the output. The small circle represents inversion.
Exclusive-OR/ XOR GATE:
The 'Exclusive-OR' gate is a circuit which will give a high output if one of its inputs is high but not
both of them. The XOR operation is represented by an encircled plus sign.
EXCLUSIVE-NOR/Equivalence GATE:
The 'Exclusive-NOR' gate is a circuit that does the inverse operation to the XOR gate. It will give a
low output if one of its inputs is high but not both of them. The small circle represents inversion.
Combinational Circuits – Karnaugh Map – Analysis and Design Procedures – Binary Adder –
Subtractor – Decimal Adder – Magnitude Comparator – Decoder – Encoder – Multiplexers –
Demultiplexers.
Logic Gates
o The logic gates are the main structural part of a digital system.
o Logic Gates are a block of hardware that produces signals of binary 1 or 0 when input logic requirements
are satisfied.
o Each gate has a distinct graphic symbol, and its operation can be described by means of algebraic
expressions.
o The seven basic logic gates include: AND, OR, XOR, NOT, NAND, NOR, and XNOR.
o The relationship between the input-output binary variables for each gate can be represented in tabular
form by a truth table.
o Each gate has one or two binary input variables designated by A and B and one binary output variable
designated by x.
AND GATE:
The AND gate is an electronic circuit which gives a high output only if all its inputs are high. The AND
operation is represented by a dot (.) sign.
OR GATE:
The OR gate is an electronic circuit which gives a high output if one or more of its inputs are high. The
operation performed by an OR gate is represented by a plus (+) sign.
NOT GATE:
The NOT gate is an electronic circuit which produces an inverted version of the input at its output. It
is also known as an Inverter.
, NAND GATE:
The NOT-AND (NAND) gate which is equal to an AND gate followed by a NOT gate. The NAND
gate gives a high output if any of the inputs are low. The NAND gate is represented by a AND gate
with a small circle on the output. The small circle represents inversion.
NOR GATE:
The NOT-OR (NOR) gate which is equal to an OR gate followed by a NOT gate. The NOR gate gives
a low output if any of the inputs are high. The NOR gate is represented by an OR gate with a small
circle on the output. The small circle represents inversion.
Exclusive-OR/ XOR GATE:
The 'Exclusive-OR' gate is a circuit which will give a high output if one of its inputs is high but not
both of them. The XOR operation is represented by an encircled plus sign.
EXCLUSIVE-NOR/Equivalence GATE:
The 'Exclusive-NOR' gate is a circuit that does the inverse operation to the XOR gate. It will give a
low output if one of its inputs is high but not both of them. The small circle represents inversion.
