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LOGIC CIRCUIT
LOGIC GATES
A logic gate is an elementary building block of a digital circuit. It processes one or more input
signal in a logical fashion. Depending on the input value or voltage, the logic gate will either
output a value of ‘1’ for ON or a value of ‘0’ for OFF.
BINARY CODE
Logic gates are digital circuits and they utilize a binary numbering system known as binary
code. Binary code is the same language used by computer which uses only 1 or 0 as numbers.
INPUTS AND OUTPUTS
Gates have two or more inputs, except a NOT gate which has only one input. All gates have
only one output. Usually the letters A, B, C and so on are used to label inputs and output.
LOGIC SYMBOL OF THE “AND” GATE
HOW DOES THE AND GATE WORK?
‘AND’ gates are like two or more switches in series. All the switches have to be closed (ON or
value of 1) in order to make the lamp (output) turn on. If all the inputs are not ‘ON’, the output is
‘OFF’.
TRUTH TABLE FOR “AND” GATE
INPUT
INPUT
OUTPUT
A
0
0
1
1
B
0
1
0
1
C
0
0
0
1
All the value of the AND gate must be a ‘1’ in order or the output value to be ‘1’. Any other input
combination will result in zero.
OR GATE
An ‘OR’ gate is like two or more switches in series. Only one switch need to be closed (ON or
value of 1) in order to make the lamp (output C) turn ON with a value of 1.
LOGIC SYMBOL FOR “OR” GATE
TRUTH TABLE OF “OR” GATE
INPUT
INPUT
OUTPUT
A
0
0
1
1
B
0
1
0
1
C
0
1
1
1
A value of ‘1’ applied to either or both inputs of the OR gate will result in an output value of ‘1’. A
value of ‘0’ applied to both inputs will result in an output of ‘0’.
NOT GATE
NOT gate have only one input and output. It reverses the input signal value. If the input is 1, the
output will be 0 and if the input is 0 then the output will be 1.
LOGIC SYMBOL FOR “NOT” GATE
TRUTH TABLE FOR “NOT” GATE
INPUT
OUTPUT
A
0
1
C
1
0
“NOT” gate can be referred as inverter, whatever the input signal is the output is always the
opposite.
LOGIC EQUATIONS
Aside representing the functioning of a logic gate with truth table and grammatical definition, the
use of logic equations can be used not only to represent logic gates and circuits, but also with
the usage of some theorems and equivalences, to reduce the number of terms involved,
simplifying the equation.
Symbolic logic uses values, variables and operations;
TRUE is represented as 1 while FALSE as 0.
Variables are represented by letters and can have one or two values, either 0 or 1. Operations
are functions of one or more variables.
AND gate equation
The AND gate operation can also be expressed by a Boolean algebraic equation. For 2 – input
AND gate, the equation is;
X = A.B
The symbol for AND gate operation is a center dot. It does not mean multiplication. The
equation read X equals to A and B, which simply mean that the output of the gate is a logic 1
when A and B inputs are in their 1 states.
OR gate equation
The Boolean algebraic equation expression is given as;
X=A+B
The equation read X equals to A or B, which simply mean that the output of the gate is a logic 1
when A or B inputs are in their 1 states.
NOT gate equation
The NOT gate operation can be expressed by a Boolean algebraic equation as;
X=A
A complement bar is placed over the assigned input letter. The expression is read as X is equal
A which simply means that the output state is opposite of the logic state applied to the input.
ALTERNATIVE LOGIC CIRCUIT
These are gates that are formed from combination of two logic gates. There are two types of
alternative logic gate:
NAND GATE
A NAND gate is the combination of an AND gate and NOT gate. It operates the same as an
AND gate but the output will be opposite. Remember, the NOT gate does not always have to be
the output leg; it could be used to invert an input signal also.
LOGIC SYMBOL FOR THE “NAND” GATE
Notice the circle on output C.
TRUTH TABLE FOR THE “NAND” GATE
INPUT
INPUT
OUTPUT
A
B
C
0
0
1
0
1
1
1
0
1
1
1
0
NAND GATE EQUATION
The NAND gate operation can also be expressed by a Boolean algebra equation. For a 2 – input
NAND gate, the equation is:
X = A.B
This equation read X equal to A and B NOT, which simply means that the output of the gate is
not a logic 1 when A and B inputs are their 1 states.
NOR GATE
A NOR gate is the combination of both an OR gate and NOT gate. It operates the same as an OR
gate, but the output will be the opposite.
TRUTH TABLE FOR THE “NOR” GATE
INPUT
INPUT
OUTPUT
A
B
C
0
0
1
0
1
0
1
0
0
1
1
0
NOR GATE EQUATION
The NOR gate operation can also be expressed by a Boolean algebra equation. For a 2 – input
NAND gate, the equation is:
X=A+B
The expression is the same as the OR gate with an over bar above the entire portion of the
equation representing the input. This equation read X equal to A or B NOT, which simply means
that the output of the gate is not a logic 1 when A or B are in their 1 states.
USES OF LOGIC GATES
Logic gates are in fact the building block of digital electronics, they are formed by the
combination of transistors (either BJT or MOSFET) to realise some digital operations like
logical OR, NOT, AND etc. Every digital product like computers, mobile phones, calculators,
even digital watches contains logical gates.
XOR GATE
The XOR (exclusive – OR) gate acts in the same way as the logical “either or”. The output is
“True” if either but not both, of the inputs are “true”. The output is “false” or if both inputs are
“true”.
LOGIC SYMBOL FOR “XOR” GATE
TRUTH TABLE FOR THE “XOR” GATE
INPUT
INPUT
OUTPUT
A
B
Y
0
0
0
0
1
1
1
0
1
1
1
0
XOR COMPARATOR
Comparator is a combinational logic circuit that compares the magnitudes of two binary
quantities to determine which one has the greater magnitude. In order word, comparator
determines the relationship of two binary quantities. A XOR can be used as basic comparator.
As you can see, the only difference between these two symbols is that the XNOR has a circle on
its output to indicate that the output is inverted.
One of the most common uses for XOR gates is to add two binary numbers. For this operation to
work, the XOR gate must be used in combination with an AND gate.
To understand how the circuit works, review how binary addition works:
0+0=0
0+1=1
1+0=1
1 + 1 = 10
If you wanted, you could write the results of
each of the preceding addition statements by
using two binary digits, like this:
0 + 0 = 00
0 + 1 = 01
1 + 0 = 01
1 + 1 = 10
When results are written with two binary digits, as in this example, you can easily see how to use
an XOR and an AND circuit in combination to perform binary addition.
If you consider just the first binary digit of each result, you’ll notice that it looks just like the
truth table for an AND circuit and that the second digit of each result looks just like the truth
table for an XOR gate.
The adder circuit has two outputs. The first is called the Sum, and the second is called the Carry.
The Carry output is important when several adders are used together to add binary numbers that
are longer than 1 bit.