is 151 - lecture 3

IS 151 Digital Circuitry 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



• Basic digital logic operations – NOT, AND,

OR, Exclusive-OR



– 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


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.


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.


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.


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 gate.


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?


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


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.


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)


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


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


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.


• End of Lecture

is 151 - lecture 3

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