Chapter 3 Combinational Logic Design

Chapter Two number system

Basic Logic Operation.

There three basic Logic operation in digital circuit. They are

1. AND Operation
2. OR Operation
3. NOT Operation

Each operation will have special symbol. The lines connected to each symbols are inputs and outputs. The inputs are on left side of symbol and output is on right side.

A circuit that performs a specified logic operation is called a logic gate.

1) AND Operation:

in AND Operation, if all the inputs are 'HIGH' then it generates 'HIGH' output, otherwise it generates 'LOW' output. It accepts two or more than two inputs and generates single output.

Truth Table:

If A and B are two inputs and Z is the output then Truth table is given as

Inputs		Output
A	B	Z=A.B
HIGH (1)	HIGH (1)	HIGH (1)
HIGH (1)	LOW (0)	LOW (0)
LOW (0)	HIGH (1)	LOW (0)
LOW (0)	LOW (0)	LOW (0)

2) OR Operation:

In OR operation, if  any of the inputs are 'HIGH' then it generates 'HIGH' output, otherwise it generates 'LOW' output. It accepts two or more than two inputs and generates single output.

Truth Table:

If A and B are the two inputs and Z is the output then the Truth Table is given as

Inputs		Output
A	B	Z=A+B
HIGH (1)	HIGH (1)	HIGH (1)
HIGH (1)	LOW (0)	HIGH (1)
LOW (0)	HIGH (1)	HIGH (1)
LOW (0)	LOW (0)	LOW (0)

3) NOT Operation:

In NOT Operation, if the input is 'HIGH' then it gives 'LOW' output and if the input is 'LOW' then it gives 'HIGH' output. It accepts single input and generates single output.

Truth Table:

If A is input and Z is output then the truth table can be expressed as

Input	Output
A	Z=A‘
HIGH (1)	LOW (0)
LOW (0)	HIGH (1)

Integrated Circuit (IC)

IC is an electronic circuit that is constructed entirely on a single small chip of silicon.
All the components that make up the circuit 
transistor, diodes, resistors and capacitors.

Different types of IC:

1) Small scale interagation (SSI):

Describes ICs having upto 10 equivalent gate circuits on a single chip and they include basic gates and Flip-flop.

2) Medium scale interagation (MSI):

Describes ICs that have 10 to 100 equivalent gates on a chip. They includes logic functions such as encoders, decoders, counters, registers, etc.

3) Large  scale interagation (LSI):

It is classfication of ICs that have from 100 to 10,000 equivalent gates on a chip including memories.

4) Very large  scale interagation (VLSI):

It describes ICs with complexity of more than 10,000 to 1,00,000 equivalent gate per chip.

5) Ultra large scale interagation (ULSI):

Describes very large memories, large microprocessor and lager single chip computers of more than 1,00,000 equivalent gates per chip.

The Clock and Timing Diagram

The Clock:

In digital system all waveforms are synchronized with a basic timing waveform called clock.
The clock is a periodic waveform in which each interval between pulses ( the period ) equals the time for one bit.
Each bit in a sequence occupies defined time interval called a bit time. When waveform is HIGH, a binary '1' is present and when waveform is LOW a binary '0' is present.

In clock waveform, each change in level of waveform A occurs at the leading edge of clock waveform. In other cases, level change occur at the trailing edge of clock waveform. The clock waveform doesnot carry any information.

Timing Diagram:

A timing diagram is a graph of digital waveforms showing the actual time relationship of two or more waveforms and how each waveform changes in relation to the others.
By looking at timing diagram, we can determine states ( HIGH or LOW ) of all the waveforms at any specified point in time and the exact time that a waveform changes state to the other waveforms.

In above example of timing diagram, the three waves A, B, C are 'HIGH' only during bit time '7' and they all change back 'LOW' at the end of bit time '7'.

Digital Signals and Waveforms

Electronic circuit can be divided into two broad catagories: Digital and Analog.
Digital electronics involves quantities with discrete values and analog electronic involves quantities with continuous values.

Fig. Analog Signal

An analog quantity is one having continious values. Most things that can be measured quantitavely occur in nature in analog form.Example of analog quantities are time, pressure, distance, sounds etc.

Fig. Digital Signal

An digital quantity is one having a discrete set of values. It is mainly used for processing within the computer. Digital data can be processed and transmitted more efficiently and reliably then analog data. It has high accuracy.

Digital Waveform:

Digital waveforms consists of voltage levels that are changing back and forth between the HIGH and LOW levels of states.

Positive going pulse is generated when the voltage or current goes from its normally LOW level to HIGH level and then back to its LOW level.

Negative going pulse is generated when the voltage goes from its normally HIGH level to its LOW level and back to its HIGH level.






A digital wavefom is made up of a series of Pulses. A pulse has two edges:

1. Leading edge: Occurs first time at t0
2. Trailing edge: Occurs last time at t1

• For a positive going pulse, the leading edge is a rising edge and trailing edge is a falling edge.
• For a negative going pulse, the leading edge is a falling edge and tariling edge is a rising edge.

Non-ideal Pulse

Rise time (tr):
time required for a pulse to go from Low to High level.

Fall time (tf):
time required for a pulse to go from High level to Low level.

Amplitude:
height of pulse from its baseline.

Pulse width (tw):
it is a measure of duration of the pulse and is often defined as the time interval between 50% points on the rising and falling edges.

Waveform Characteristics

Most waveforms encountered in digital system are composed of series of pulses, sometimes called pulse trains, can be classified as
Periodic
Non-Periodic

A periodic pulse waveform is one, that repeats itself at a fixed interval called a Time Period (T). The frequency (f) is the rate at which it repeats itself and is measured in Hertz (Hz)

Period = T1 = T2 = T3 = ......... = Tn

frequency (f) = 1/T

A non-periodic pulse waveform doesnot repeat itself at fixed interval and may be composed of pulses with ramdomly differing pulse width and randomly differing time interval between the pulses.




The frequency of a pulse is the reciprocal of the period. The relation between frequency and time period is expressed as
f = 1/T
T = 1/f

Duty Cycle:

An important characteristics of a periodic digital waveform is its duty cycle, which is the ratio of the pulse width (tw) to the period (T). It can be expressed as a percentage.

Duty Cycle = (tw/T)*100%

Parity Generator/Checker

Types of Parity:

1) Even Parity:

• if the number of '1' is even in original signal then it is called even parity.

example:

Original Signal	Parity
a)    0100	1
b)    1100	0

2) Odd Parity:

• if the numbre of '1' is odd in original signal then it is called odd parity.

example:

Original Signal	Parity
a)    0100	0
b)    1100	1

Even Parity Generator:

Message
A	B	C	P(Parity)
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	1
1	0	1	0
1	1	0	0
1	1	1	1

Even Parity Checker:

Received Message
x	y	z	p	C
0	0	0	0	0
0	0	0	1	1
0	0	1	0	1
0	0	1	1	0
0	1	0	0	1
0	1	0	1	0
0	1	1	0	0
0	1	1	1	1
1	0	0	0	1
1	0	0	1	0
1	0	1	0	0
1	0	1	1	1
1	1	0	0	0
1	1	0	1	1
1	1	1	0	1
1	1	1	1	0

Odd Parity Generator:

Message
A	B	C	P(Parity)
0	0	0	1
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	0

Odd Parity Checker:

Received Message
x	y	z	p	C
0	0	0	0	1
0	0	0	1	0
0	0	1	0	0
0	0	1	1	1
0	1	0	0	0
0	1	0	1	1
0	1	1	0	1
0	1	1	1	0
1	0	0	0	0
1	0	0	1	1
1	0	1	0	1
1	0	1	1	0
1	1	0	0	1
1	1	0	1	0
1	1	1	0	0
1	1	1	1	1