IS 151 Lecture 3 - 2014/2015

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
IS 151 Digital Circuitry 1

2. Basic Logic Operations
• Basic digital logic operations – NOT, AND,
OR, Exclusive-OR
IS 151 Digital Circuitry 2

3. Basic Logic Operations
IS 151 Digital Circuitry 3
– 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

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.
IS 151 Digital Circuitry 4

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.
IS 151 Digital Circuitry 5

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.
IS 151 Digital Circuitry 6

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 EX-OR
IS 151 Digital Circuitry 7
gate.

8. Logic Operations - Review
1. When does the NOT operation produce a HIGH/LOW
IS 151 Digital Circuitry 8
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?

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
IS 151 Digital Circuitry 9

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.
IS 151 Digital Circuitry 10

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)
IS 151 Digital Circuitry 11

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
IS 151 Digital Circuitry 12

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
IS 151 Digital Circuitry 13

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.
IS 151 Digital Circuitry 14

15. • End of Lecture
IS 151 Digital Circuitry 15