Chapter 4 cont...

A transistor has three terminals
- A source
- A base
- An emitter, typically connected to a ground wire

If the electrical signal is grounded, it is allowed to flow through an alternative route to the ground (literally) where it can do no harm.

The easiest gates to create are the NOT, NAND, and NOR gates.

Combination circuit
The input values explicitly determine the output

Sequential circuit
The output is a function of the input values and the existing state of the circuit.
We describe the circuit operations using: Boolean expressions, Logic diagrams, and Truth tables.

Combinational Circuits
Gates are combined into circuits by using the output of one gate as the input for another.

Three inputs require eight rows to describe all possible input combinations. This same circuit using a Boolean expression is (AB + AC).

Consider the following Boolean expression A(B+C) "+ means or"

Circuit equivalence
Two circuits that produce the same output for identical input

Boolean algebra allows us to apply provable mathematical principles to help design circuits.

A(B+C)=AB+BC (distributive law) so circuits must be equivalent.

<u>Properties of Boolean Algebra</u>
Commutative AB=BA
Associated (AB)C=A(BC)
Distributive A(B+C)=(AB)+(AC)
Identity A1=A
Complement A(A')=0
DeMorgan's law (AB)'=A' OR B'

Adders

At the digital logic level, addition is performed in binary.

The result of adding two binary digits could produce a carry value

Recall that 1+1=10 in base two

Half adder
A circuit that computers the sum of two bits and produces the correct carry bit.

Circuit diagram representing a half adder.

Boolean expressions sum = A (+) B carry = AB    "(+) means exclusive or"

Full adder
A circuit that takes the carry-in value into account.

Multiplexer
A circuit that uses a few input control signals to determine which of several output data lines is routed to its output.

Circuits as Memory
Digital circuits can be used to store information.
The circuits form a dequential circuit....etcccccccc

Integrated circuit (also called a chip)

A piece of silicon on which multiple gates have been embedded.

Silicon pieces are mounted on a plastic ceramic package with pins along the edges that can be soldered onto circuit boards or inserted into appropriate sockets.

Integrated circuits (IC) are classified by the number of gates contained in them.

SSI Smal-Scale Integration 1 - 10 gates
MSI Medium-Scale Integration 10 - 100 gates
LSI Large Scale -100 - 100,000
VLSI Very-Large-Scale more than 100,000

CPU Chips
The most important integrated circuit in any computer is the Central Preocessing Unit, or CPU....etc