Gate-
A device that performs a basic operation on electrical signals
Circuits -
Gates combined to perform more complicated tasks
Boolean expressions
Uses Boolean algebra, a mathematical notation for expressing two; calculated logic
Logic diagrams
A graphical representation of a circuit; each gate has its own symbol
Truth tables
A table showing all possible input value and the associated output values.
Six types of gates
-NOT
-AND
-OR
-XOR
-NAND
-NOR
Typically, logic diagrams are black and white with gates distinguished only by their shape.
We use color for emphasis (and fun)
**fun...psssft yeah right.
A NOT gate accepts one input signal (0 or 1) and returns the opposite signal as output.
Triangle small circle
Boolean expression X = A'
Truth table
A X
0 1
1 0
An AND gate accepts two input signals
If both are 1, the output is 1; otherwise, the output is 0
Boolean expression X= A x B
A
D (looking shape) X
B
Truth table
A B X
0 0 0
0 1 0
1 0 0
1 1 1
An OR gate accepts two input signals
If both are 0, the output is 0; otherwise, the output is 1
Boolean Expression X = A + B
A
Fin looking shape X
B
Truth Table
A B X
0 0 0
0 1 1
1 0 1
1 1 1
An XOR gate accepts two input signals Exclusive OR
If both are the same, the output is; otherwise, the output is 1
Boolean Expression X A (+) B
A
) Fin shape X
B
Truth Table
A B X
0 0 0
0 1 1
1 0 1
1 1 0
Note the difference between the XOR gate and the OR gate; they differ only in one input situation.
The NAND gate accepts two input signals
If both are 1, the output is 0; otherwise, the output is 1
Boolean Expression X = (A x B)'
A
Dsmall circle X
B
Truth Table
A B X
0 0 1
0 1 1
1 0 1
1 1 0
The NOR gate accepts two input signals
If both are 0, the output is 1; otherwise, the output is 0
Boolean Expression X = (A + B) '
A
Fin shape Small Circle X
B
Truth Table
A B X
0 0 1
0 1 0
1 0 0
1 1 0
A NOT gate inverts its single input
AN AND gate produces 1 if both input values are 1
AN OR ate produces 0 if both input values are 0
An XOR gate prodcuces 0 if input values are the same
A NAND gate prodcuces 0 if both inputs are 1
A NOR gate produces a 1 if both inputs are 0
Gates with more inputs
Gates can be desgined to accept three or more input values
A three-iunput AND gate, for exampl, prodcuces and output of 1 only if all input values are 1
Boolean Expression X = A x B x C
A
B D shape X
C
Truth Table
A B C X
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
etcccccc
Constructing Gates
Transitor
A device that acts either as a wire that conducts electicity or as a resitor that blocks the flow of electricity, depending on the voltage level of an input signal
A transitor has no moving parts, yet acts like a switch
It is made of a semiconductor material, which is neither a particulary good conductor of electricity nor a particularly good insulator.