Scribd
Upload
59 views18 pages

2 CMOSLogic

1) Digital circuits use binary digits (0s and 1s) to represent information, with different voltage levels representing 0 and 1. 2) Combinational logic circuits have outputs that are a function of the current inputs only, and are used to restore valid signal levels. 3) Basic logic gates like AND, OR, and NOT can be implemented using transistor switches, and more complex functions can be built by combining gates. For example, a full adder circuit for adding two binary numbers can be designed using logic gates.

Uploaded by

arcticstrat
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
59 views18 pages

2 CMOSLogic

1) Digital circuits use binary digits (0s and 1s) to represent information, with different voltage levels representing 0 and 1. 2) Combinational logic circuits have outputs that are a function of the current inputs only, and are used to restore valid signal levels. 3) Basic logic gates like AND, OR, and NOT can be implemented using transistor switches, and more complex functions can be built by combining gates. For example, a full adder circuit for adding two binary numbers can be designed using logic gates.

Uploaded by

arcticstrat
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 18

Building A Computer

Inform a tion is encod ed w ith bits: 0 's a nd 1's .

(we've already seen 2's com plem ent num bers)

These a re encod ed using + w ell und erstood

voltages...

+ ea s y to genera te, d etect - a ffected b y environm ent

B ut w hy 1's a nd 0 's only?

Digital Representation
Example: representing a B&W picture: Black = 0 V White = 1 V 80% grey = 0.8 V ... Represent by scanning picture in xed order. Let's try doing some computation with the voltages...

Digital Representation
Flip image:
Flip back and forth...

What really happens...

Have to build system to tolerate some error (noise).

Logic Levels

Store just one bit on a wire... Gain reliability

0V
"unknown"

3.3V

anything here is logic level 0

anything here is logic level 1

Different conventions are possible


5V
"unknown"

5V

anything here is logic level 1

anything here is logic level 0

Combinational Devices

A combinational device: Output is a function of inputs only ("memoryless") Takes input to valid, stable outputs Combinational devices restore marginally valid signals!
valid input logic 0 0V valid input logic 1 3.3V

valid output logic 0

noise margin

valid output logic 1

Example

Input: logic 0 if O utput logic 0

< Vil , logic 1 if < Vol , logic


Vih Voh
Vin

if 1

> Vih if > Voh

3.3V

Vil

Vout

Vout avoid these regions!

Vol
0V 3.3V

Vin

Digital View

If input is 0 , output is 1 If input is 1, output is 0

N orm a lly w ritten in a ta b le, like this :

In 0 1

O ut 1 0

C a lled a "truth-ta b le".

Im p le m e n t a t io n : S w itc h in g N e t w o rks

Lots of ways to build switches... relays vacuum tubes transistors ...


Ptransistor
a g b g

Ntransistor
a

Connect a and b if g = 0.

Connect a and b if g = 1.

Switching Networks: Inverter


Vdd

in
in out

out 1 0

0 1

GND

Function: NOT Called an inverter Symbol:


in out

Switching Networks: NAND


Vdd

a
a

b out 0 0 1 1 1 1 1 0

0
out

1 0
b

GND

Function: NAND Symbol:


a out b

Switching Networks: NOR


Vdd b

a
a out

b out 0 0 1 1 1 0 0 0

0 1 0 1

GND

Function: NOR Symbol:


a out b

Building Functions From Gates

AND:
=

OR:
=

Can specify function by describing gates, truth table, or logic equations.

Logic Equations

AND:

out = a b out = ab out = a b

OR: NOT:

out = a + b out = a b

out = in out = in

Logic Equations
Fun with identities:
a+a=1 a+0=a a+1=1

aa = 0 a0=0 a1=a a(b + c) = ab + ac (a + b) = a b (a b) = a + b a + ab = a + b

Check by writing truth tables, or by manipulating logic equations.

Let's Build An Adder

Write down function: Two 1-bit inputs, a and b Two 1-bit outputs, sum and carry Truth-table: a 0 1 0 1 b carry sum 0 0 0 0 0 1 1 0 1 1 1 0

Let's Build An Adder

Sum output: a 0 1 0 1 Logic equation: Circuit:


a b a b ab

b sum Logic term 0 0 ab 0 1 ab 1 1 ab 1 0 ab


ab ab + ab

ab+ab

Let's Build An Adder


Carry output: a 0 1 0 1 Logic equation: Circuit: b carry Logic term 0 0 ab 0 0 ab 1 0 ab 1 1 ab
ab
a b ab

Let's Build An Adder


Final Circuit:
+0 +0

a b

ab

+2

carry

a b a b

ab
+3 +3

ab + ab
+5

sum

ab

Numbers indicate the number of sequential steps from input to output (worst-case).

You might also like