Chapter 4 Gates and Circuits

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.