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8/10/2019 Tutorial_ Digital Circuits-Elemental Digital Circuits, Renesas Engineer School _ Renesas Electronics Europe

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Tutorial: Digital Circuits-Elemental Digital Circuits, Renesas Engineer School

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Analog vs. Digital: Whats the Difference?

Air temperature, sound loudness, light intensityin nature, all of these quantities vary smoothly and

continuously over a range. Such quantities is called "analog" value.

Todays computers, in contrast, work with discrete quantities. These discrete quantities are called

"digital" values. Where an analog measurement is a smooth curve that " looks like" the measured

property, digital measurements are a series of discontinuous levels.

Heres another way to put it: analog values are real numbers, whereas digital values are integers.

Real numbers can represent any point on a number line, whereas integer are limited to expressthose special points evenly spaced on the line.

An analog circuit works with analog signalswhere values change continuously. A digital c ircuit

works with digital signals, where all values are discrete.

Figure 1 : Analog vs. Digital

To input natures analog information into digital circuits, it is first necessary to digitize the

information: that is, to convert the analog signal into a digital signal. An analog/digital (A/D)

converter samples the analog signal (reads the value at a set time interval), and converts each

reading into a corresponding binary number (a base 2 value, expressed in 0s and 1s).

Since the converter is changing an analog signal that can take any fractional value into a digital

signal that can take discrete values only, some information will be lost. Each analog reading mustbe rounded up or down to the nearest digital value. And since the converter reads the analog signal

at a specific interval only, it loses the analog information that exists between these intervals.

As a result, digital v alues are only an approximation of the analog signal and always contain

conversion error. This error can be reduced, however, by shortening the interval between

measurements, and by using more precise (that is, longer bit-length) digital values.
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But whats the point of converting a smooth analog signal into a jumpy and imprecise series of

numbers? There are at least two advantages: digital signals are much more resistant to noise; and,

because modern computers work with digital values only.

Todays powerful microcontrollers are capable of rapidly processing large volumes of digital

information. These microcontrollers use digital circuits that take full advantage of the fact that,

unlike analog signals, digital signals do not lose information during transmission and playback.

Digital Circuits = Logic Circuits

A digital c ircuit, also called a logic circuit, carries out a logical operation. Three elemental circuits

AND, OR, and NOTcan be combined to build any desired logical operation.

Logic circuits are expressed using logical expressions and circuit symbols. (Here we use MIL

symbols, although JIS symbols or other symbologies may be used instead.) A truth table indicates

what the circuits output will be for all combination of inputs.

The AND Circuit, A Series Circuit

An AND circuit, also called a logical product circuit, take two inputs, and outputs a 1 i f both inputs

are 1, and a 0 otherwise.

Logical Expression of AND

Written using the " " operator. Example: Y = AB

Circuit Notation

Binary Numbers

Digital signals typically express values using binary (also called " base 2" ) numbering, where each

number is written using only 0s and 1s. Specifically, the rightmost digit of the number represents

20 , the next digit to the left represents 2 1 , then 2 2 , etc. A four-digit binary number, therefore, canrepresent 16 values, from 0 to 15, as you can see in the Table 1. Values higher than 15 can be

represented by adding additional digits, as necessary.

Decimal Binary

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

10 1010

11 1011

12 1100

13 1101

14 1110

15 1111

Table 1: Binary Representation of Decimal Values

One advantage of treating digital signals as binaries is that it is easy to design logic circuits with

binary output: the circuits are either ON or OFF, corresponding to the 1s and 0s of numeric binary

numbers. The ON and OFF states are physically implemented as two voltage states: high (" H" ) and

low (" L" ). In a typical CMOS IC with a 5-volt power source, " L" denotes a voltage from 0 up to 1.35

V, while " H" denotes a voltage from 3.15 V on up. Because 0 and 1 correspond to these relatively

wide voltage ranges, the circuit produces the correct output even when there is moderate noise on

the line.


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Truth Table

A B Y

0 0 0

0 1 0

1 0 0

1 1 1

Lets look at how an AND circuit works. Figure 2 shows an AND circuit comprising two switches

(SW A and SW B) and a LED indicator. Note that:

SW A is On if input A is 1; SW A is Off if input A is 0. SW B is On if input B is 1; SW B is Off if input B is 0.

LED Y is On (lit) if output Y is 1; LED Y is Off (dark) if output Y is 0

Figure 2: An AND Circuit

This AND circuit works as follows.

If SW A and SW B are both On, then LED Y is On (lit).

If one switch is On but the other is Off, then LED Y is Off (dark).

If both switches are Off, then LED Y is Off (dark).

Basic logic circuits are also called gates. Note that you can control the value of the output by

leaving one switch closed while controlling the other switch. Figure 2 illustrates the AND circuits

gate operation.

If either SW A or SW B is fixed at Off, the LED will remain dark; that is, the output will also be

fixed at Off (the gate is closed).

If either SW A or SW B is fixed at On, then the gate will output the value of the unfixed SW (thegate is open).

The OR Circuit, A Parallel Circuit

An OR circuit , also called a " logical sum circuit, " outputs a 1 if either or both inputs are 1, and

outputs a 0 if both inputs are 0. Example: Y = A+B.

Logical Expression of OR

Written using the " +" operator. Example: Y = A+B

Circuit Notation

Truth Table

A B Y

0 0 0

0 1 1

1 0 1

1 1 1

Figure 3 shows an OR circuit: a parallel circuit with two switches and one LED indicator.

Since this a parallel circuit, the output will be On (LED Y will light up) if only SW A, only SW B, or

both SW A and SW B are On.

The gate operation of the OR circuit is the reverse of the AND circuits operation.

If either SW A or SW B is fixed at On, the LED will light; that is, the output will also be fixed at On

(the gate is closed).

If either SW A or SW B is fixed at Off, the gate will output the value of the unfixed SW (the gate is

open)


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Next time we will look at how digital ICs work.

Digital CircuitsPart 2: Digital ICs and Combinational Logic

Figure 3: An OR Circuit

The NOT Circuit, An Inverter Circuit

A NOT ci rcuit (also called an " inverter circuit," ) takes only one input, and outputs the inverse of

the input. If the input is 1, the output is 0. If the input is 0, the output is 1.

Logical Expression of NOT

Written using the " " operator. Example: Y =

Circuit Notation

Truth Table

A Y

0 1

1 0

Back To Top

Create the truth table of this logic circuit:

(Note: The priority of logic operators: NOT, AND, OR.)

Answer50k

Gain of the inverting amplification circuit is: A = R 2 /R 1 . Also, 5R 2 /10 k. Consequently,

R2 = 50 k.
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