- Week 6 Gates and Circuits PART I
- READING Chapter 4

Gates and Circuits

EECS 1520 -- Computer Use Fundamentals

- What is a gate?
- A gate is a device that performs a basic

operation on electrical signals

- What is circuit?
- Gates are combined to form different circuits

to perform more complicated tasks

Gates and Circuits

EECS 1520 -- Computer Use Fundamentals

- Three notational methods to describe the behavior

of gates - Boolean expressions A form of algebra in which

variables and functions take on only one of two

possible values (0 and 1) - Logic diagrams graphical representation of a

circuit - Truth tables defines the function of a gate by

listing all possible input combination and the

corresponding output.

Gates and Circuits

EECS 1520 -- Computer Use Fundamentals

- A gate or logic gate performs only one logical

function. Each gate accepts one or more input

values and produces a single output value.

- Six types of logic gates
- NOT
- AND
- OR
- XOR
- NAND
- NOR

Gates and Circuits NOT Gate

EECS 1520 -- Computer Use Fundamentals

- Also referred to as an inverter
- If the input value is 1, the output is 0 if the

input value is 0, the output is 1

Logic diagram Symbol

Truth Table

Boolean Expression

- Sometimes the mark is replaced by

horizontal bar placed over the value

Gates and Circuits AND Gate

EECS 1520 -- Computer Use Fundamentals

- If the two input values are both 1, the output is

1 otherwise, the output is 0

Logic diagram Symbol

Truth Table

Boolean Expression

- Sometimes the . mark is replaced by the

asterisk symbol

Gates and Circuits OR Gate

EECS 1520 -- Computer Use Fundamentals

- If both input values are both 0, the output is 0

otherwise, the output is 1

Logic diagram Symbol

Truth Table

Boolean Expression

Gates and Circuits XOR or exclusive OR Gate

EECS 1520 -- Computer Use Fundamentals

- If the two inputs are the same, the output is 0

otherwise, the output is 1

Logic diagram Symbol

Truth Table

Boolean Expression

- Not the difference between the XOR gate and the

OR gate they only differ in one input situation - When both input signals are 1, OR gate produces a

1 and the XOR gate produces a 0

Gates and Circuits NOR Gate

EECS 1520 -- Computer Use Fundamentals

- The NOR gate is essentially the opposite of the

OR gate. That is, the output of a NOR gate is

the same as if you took the output of an OR gate

and put it through a NOT gate

Logic diagram Symbol

Truth Table

Boolean Expression

Gates and Circuits NAND Gate

EECS 1520 -- Computer Use Fundamentals

- The NAND gate is the opposite of the AND gate.

Logic diagram Symbol

Truth Table

Boolean Expression

Transistors

EECS 1520 -- Computer Use Fundamentals

- How do we implement the gates?
- A gate uses one or more transistors to establish

how the input values map to the output value - A transistor acts like a switch.
- It either turns on to conduct electricity or

turns off to block the flow of electricity

Transistors

EECS 1520 -- Computer Use Fundamentals

- A transistor has three terminals source, base

and emitter

source

output

base

emitter

- When an electrical signal is grounded, it has 0

volts! - If the source signal is pulled to ground, the

output signal is low output is 0 - If the source signal remains high, the output

signal is high output is 1

Transistors NOT Gate

EECS 1520 -- Computer Use Fundamentals

- The output is determined by the base electrical

signal.

source

Vout

Vin Vout

1 0

0 1

base

Vin

emitter

- If Vin is high, the source is pulled to ground

and Vout is low (i.e. 0) - If Vin is low, the source is not grounded and

Vout is high (i.e. 1)

NOT Gate needs 1 transistor

Transistors NAND Gate

EECS 1520 -- Computer Use Fundamentals

source

Vout

Vin1 Vin2 Vout

0 0 1

0 1 1

1 0 1

1 1 0

Vin1

Vin2

emitter

- If Vin1 and Vin2 are high, the source is pulled

to ground and Vout is low (i.e. 0) - If Vin1 and Vin2 are low, the source is not

grounded and Vout is high (i.e. 1) - If either Vin1 or Vin2 is low, the source is not

grounded and Vout is high (i.e. 1)

NAND Gate needs 2 transistors

Transistors NOR Gate

EECS 1520 -- Computer Use Fundamentals

source

Vin1 Vin2 Vout

0 0 1

0 1 0

1 0 0

1 1 0

Vout

Vin1

Vin2

emitter

emitter

- If Vin1 and Vin2 are high, the source is pulled

to ground and Vout is low (i.e. 0) - If Vin1 and Vin2 are low, the source is not

grounded and Vout is high (i.e. 1) - If either Vin1 or Vin2 is low, the source is

grounded and Vout is low (i.e. 0)

NOR Gate needs 2 transistors

Transistors OR Gate

EECS 1520 -- Computer Use Fundamentals

- Since OR gate is the opposite of NOR gate, how

many transistors would you think will be required

to implement the OR gate?

OR Gate needs 3 transistors

Combinational Circuits

EECS 1520 -- Computer Use Fundamentals

- Gates are combined into circuits by using the

output of one gate as the input for another gate. - For example

Combinational Circuits

EECS 1520 -- Computer Use Fundamentals

- For example

Logic diagram Symbol

Truth Table

- Since there are 3 inputs, there are 8 possible

outcomes

Combinational Circuits

EECS 1520 -- Computer Use Fundamentals

- For example

Logic diagram Symbol

Boolean expression

- D A B
- E AC
- X AB AC

Combinational Circuits

EECS 1520 -- Computer Use Fundamentals

- Now, we want to investigate the following Boolean

expression

X A(BC)

- How do we want to create the logic diagram

(called circuit 2) of the above Boolean

expression?

- We have an inner function which consists of an

OR gate between B and C - We then have an

outer function which is an AND gate between

A and (BC)

Logic diagram Symbol (circuit 2)

A(BC)

BC

Combinational Circuits

EECS 1520 -- Computer Use Fundamentals

- We have the following

X A(BC)

Boolean expression

Logic diagram Symbol

A(BC)

BC

A B C BC A(BC)

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

A B C BC A(BC)

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1

A B C BC A(BC)

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 1 0

1 0 0 0 0

1 0 1 1 1

1 1 0 1 1

1 1 1 1 1

Truth table

Combinational Circuits

EECS 1520 -- Computer Use Fundamentals

- Circuit 1

- Circuit 2

A(BC)

BC

A B C BC A(BC)

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 1 0

1 0 0 0 0

1 0 1 1 1

1 1 0 1 1

1 1 1 1 1

A B C D E X

0 0 0 0 0 0

0 0 1 0 0 0

0 1 0 0 0 0

0 1 1 0 0 0

1 0 0 0 0 0

1 0 1 0 1 1

1 1 0 1 0 1

1 1 1 1 1 1

- Their results are identical!

Combinational Circuits

EECS 1520 -- Computer Use Fundamentals

- We have therefore demonstrated circuit equivalence

- That is, both circuits produce the same results

for each input combination

- Boolean algebra allows us to apply provable

mathematical principles to help us design logical

circuits

- From the previous example

X AB AC A(BC)

Properties of Boolean Algebra

EECS 1520 -- Computer Use Fundamentals

- DeMorgans law, in particular, is very useful in

Boolean algebra.

- For instance, it means that

___ ___ ___

1 NAND gate is equivalent to 2 NOT gates with an

OR gate