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Digital signal

digital signal has two binary levels.

0     &     1...logical int

some times these levels are refered to as

 low	&	high
 off	&	on
 false	&	true

where LOW is 0 HIGH is 1
OFF is 0 ON is 1 FALSE is 0 TRUE is 1

In didgital signals 0 represents	0 to 0.8Volts
A 1 represents	                        2.4 to 5Volts
anything between these two values are invalid

forexample: a 1.8V is not a digital signal

Investigating various type of logic gates

Three basic logic gates:

a: OR gate
b: AND gate
c: NOT gate (inverter)

Universal gates:

a: NAND gate (not and)
b: NOR gate (not or)

Truth table (characteristic table)

Each logic gates has it's own unique characteristic. They react differently with different inputs. please find below the characteristic table for each gate.

"AND" gate truth table:

The easier way to remember the AND gate truth table is that think of AND gate as a multiplication. As you should know that anything multiplied with zero, results in zero. That is how AND gate works, if any input of AND gate is zero or 0 to 0.8Volts the output is zero. WE only get a 1 or a high at the output if all the inputs are high or 1. Please see the table below to better understand how an AND gate behaves with different inputs.

Below you can find the schematic representation of a two input AND gate followed by its truth table

2 Inputs "AND" gate truth table
INPUT A	INPUT B	OUTPUT
0	0	0
0	1	0
1	0	0
1	1	1

The inputs of an AND gate is independent, the output is dependent(depend on the input)
As you can see from the above table, the output is 0 if any of the inputs are 0. the output is 1 only if all of the input are 1

Below you can find the schematic representation of a three input AND gate followed by its truth table

3 Inputs "AND" gate truth table
INPUT A	INPUT B	INPUT C	OUTPUT
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	0
1	0	0	0
1	0	1	0
1	1	0	0
1	1	1	1

You can see again from above table that the output is 1 if and only if all the inputs are 1. this is more closer to multiplication process.

"NAND" gate truth table:-

The output of a NAND gate will be 1 if any of its input is low (0)
A easier way to remember the truth table for this gate is that NAND gate behaves exactly the opposite of AND gate.
the schematic representation of a NAND get is almost exactly the same as a AND gate with the exception of a bubble at the out put. NAND gate has a bubble at the output.

scroll down to see the schematic representation of a two input NAND gate followed by its truth table

2 Inputs "NAND" gate truth table
INPUT A	INPUT B	OUTPUT
0	0	1
0	1	1
1	0	1
1	1	0

see below for schematic representation of a 3 input NAND gate followed by truth table

3 Inputs "NAND" gate truth table
INPUT A	INPUT B	INPUT C	OUTPUT
0	0	0	1
0	0	1	1
0	1	0	1
0	1	1	1
1	0	0	1
1	0	1	1
1	1	0	1
1	1	1	0

You can see from the above tables that as long as there is a 0 present in the input the output is a one, the output is low or 0 if only if all the inputs are high.....

"OR" gate truth table:-

well for me to remember the truth table for "OR" gate is to think of addition 1+0 = 1, so whenever is see a 1 in the input of a "OR" gate no matter what the other inputs are i automatically know that the output going to be a 1 or high (2.4 to 5volts)

Please find below the schematic representation of a two inputs OR gate followed by its truth table

2 Inputs "OR" gate truth table
INPUT A	INPUT B	OUTPUT
0	0	0
0	1	1
1	0	1
1	1	1

And of course the three input "OR" gate with schematic representation

3 Inputs "OR" gate truth table
INPUT A	INPUT B	INPUT C	OUTPUT
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	1
1	0	0	1
1	0	1	1
1	1	0	1
1	1	1	1

"NOR" gate truth table:-

NOR gate is just the opposite of OR gate, any 1 or high in the input will result in a low or 0 output. the output is only high if and only if all the inputs are low.

Please find below the schematic representation of a two inputs NOR gate followed by its truth table

2 Inputs "NOR" gate truth table
INPUT A	INPUT B	OUTPUT
0	0	1
0	1	0
1	0	0
1	1	0

schematic representation and Truth table for three inputs "NOR" gate, see below

3 Inputs "NOR" gate truth table
INPUT A	INPUT B	INPUT C	OUTPUT
0	0	0	1
0	0	1	0
0	1	0	0
0	1	1	0
1	0	0	0
1	0	1	0
1	1	0	0
1	1	1	0

"XOR" gate truth table:-

"XOR" gate always have only two inputs. "XOR" means either this or that but not both.

Please see the schematic representation and truth table below to better understand it.

2 Inputs "XOR" gate truth table
INPUT A	INPUT B	OUTPUT
0	0	0
0	1	1
1	0	1
1	1	0

You can see that you only get a high or 1 if the inputs are either this or that but not both. this means that the output of an "XOR" gate will always be low if both the inputs are the same.

BOOLEAN ALGEBRA

Boolean algebra is based on three logic operations

NOT
AND
OR

Based also on two logic levels

Logic "1" or true (T)
Logic "0" or false (F)

Boolean algebra has various logic laws and rules, they are as follow

Low of combination
commutetive law
Associative law
Distributive law
Law of obserption Please scroll down to see the actual circuit diagram......