The document discusses basic logic operations and logic gates. It explains that logic operations like AND, OR, and NOT are performed by logic gates and manipulate binary inputs to produce binary outputs. The AND gate produces a HIGH output only if all inputs are HIGH. The OR gate produces a HIGH output if any input is HIGH. The NOT gate inverts the input. More complex logic functions can be built by combining these basic logic gates, including arithmetic operations, comparisons, encoding, decoding, data selection, storage, and counting.

1. Basic Logic Operations
• Basic Logic Operations
– Several propositions combined form
propositional/logic functions
– Example: “The light is on” will be true if
• “The bulb is not burned out” is true and if
• “The switch is on” is true.
– Logical statement: The light is on if and only if the
bulb is not burned out and the switch is on
– The first statement (the light is on – basic proposition)
is true only if the last two statements (conditions) are
true
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2. Basic Logic Operations
• Basic digital logic operations – NOT, AND,
OR, Exclusive-OR
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3. Basic Logic Operations
– Features
• Inputs – are on the left
• Output – is on the right
– A circuit that performs a specific logic
operation is called a logic gate
– The true/false conditions are represented by a
HIGH (true) and a LOW (false)
• HIGH = TRUE = 1
• LOW = FALSE = 0
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4. The NOT operation
• Changes one logic level to the opposite
logic level
• When the input is HIGH, the output is
LOW and vice versa
• The NOT operation is implemented by a
logic circuit called an inverter.
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5. The AND operation
• Produces a HIGH output if and only if all
the inputs are HIGH
• If one input is HIGH and the other is LOW,
or all inputs are LOW, the output is LOW
• The AND operation is implemented by a
logic circuit called an AND gate.
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6. The OR operation
• Produces a HIGH output when any of the
inputs is HIGH
• Otherwise if all inputs are LOW then the
output is LOW
• The OR operation is implemented by a
logic gate called an OR gate.
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7. The Exclusive-OR operation
• Produces a HIGH output when one and
only one of the two inputs is HIGH
• The Exclusive-OR operation is
implemented by a logic gate called an EXOR gate.
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8. Logic Operations - Review
1. When does the NOT operation produce a HIGH/LOW
output?
2. When does the AND operation produce a HIGH/LOW
output?
3. When does the OR operation produce a HIGH/LOW
output?
4. When does the EX-OR operation produce a HIGH/LOW
output?
5. What is an inverter?
6. What is a logic gate?
7. What is the difference between an OR and an
Exclusive-OR operation?
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9. Basic Logic Functions
• The basic logic gates can be combined to
form more complex logic circuits that
perform many useful operations to build up
complete digital systems
• Some common logic functions:
comparison, arithmetic, code conversion,
encoding, decoding, data selection,
storage, and counting
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10. The Comparison Function
• Magnitude comparison is performed by a
logic circuit called the comparator.
• A comparator compares two quantities and
indicates whether or not they are equal.
• Example: given two numbers, determine if
the numbers are equal, and if not equal,
which one is greater.
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11. Arithmetic Functions
• Addition – performed by an adder; adds two
binary numbers (two inputs and a carry in) and
generates an output and a carry out
• Subtraction – performed by a subtracter; three
inputs: two numbers and a borrow input;
generates the difference and borrow out
• Multiplication – performed by a multiplier; have
two inputs, and an output (product)
• Division – performed by a series of
subtractions, comparisons and shifts; have two
inputs and two outputs (quotient and reminder)
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12. Code Functions
• The Code conversion function
– Changes a form of coded information into
another coded form
• The Encoding function
– Converts information into some coded form
• The Decoding function
– Converts coded information into a
nonencoded form
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13. The Data Selection Functions
• Multiplexer – switches digital data from
several input lines onto a single output line
in a specified time sequence
• Demultiplexer – switches digital data from
one input line to several output lines in a
specified time sequence
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14. Storage and Counting Functions
• The Storage function
– To retain binary data for a period of time; e.g.
flip-flops, registers
• The Counting function
– To count events represented by changing
levels or pulses or to generate particular code
sequence.
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15. • End of Lecture
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