Digital Electronics

In digital computers, everything (including letters, words and whole texts) is represented in binary numbers (zero and one) i.e., it stores data in terms of bits. Binary logic is the basis of electronic systems, such as computers and cell phones. It works on 0’s and 1’s.An electronic circuit that is designed for two-state operation is called a digital circuit.

A signal(voltage or current) which can have only two discrete values is called a digital signal. For example, a squarewave is a digital signal. The branch of electronics which deals with digital circuits is called digital electronics.

A continuously varying signal (voltage or current)is called an analog signal. For example,a sinusoidal voltage is an analog signal. In an analog electronic circuit, theoutput voltage changes continuously according to theinput voltage variations. In other words, the output voltage can have an infinite number of values.

Analog and Digital Signals

(i) Analog signal: A continuously varying signal (voltage or current) is called an analog signal.For example, an alternating voltage varying sinusoidally is an analog signal. If such an analog signal is applied to the input of a transistor amplifier, the output voltage will also vary sinusoidally. This is the analog operation i.e., the output voltage can have an infinite number ofvalues. Due to many-valued output, the analog operation is less reliable.

(ii) Digital signal: A signal (voltage or current) that can have only two discrete values is called a digital signal. For example, a square wave is a digital signal. It is because this signal hasonly two values viz, +5 V and 0 V and no other value. These values are labelled as High and Low. The High voltage is + 5 V and the Low voltage is 0 V. If proper digital signal is applied to the input of a transistor, the transistor can be driven between cut off and saturation. In other words, the transistor will have two-state operations i.e., output is either low or high. Since digital operation has only two states(i.e., ON or OFF), it is far more reliable than many-valued analog operation. It is because with two states operation, all the signals are easily recognised as either low or high.

Advantages of Digital systems

Relatively much easier to design

Digital systems can be progtammable.

Digital systems can tolarate signal variations(Noise immunity)

Easier storage of data

Ease of fabrication in integrated circuit form, leading to availability of more complex functions in a smaller size

The real world, however, is analogue. Most physical quantities – position, velocity, acceleration, force, pressure, temperature and flowrate, for example – are analogue in nature. That is why analogue variables representing these quantities need to be digitized or discretized at the input if we want to benefit from the features and facilities that come with the use of digital techniques.

Digital Circuit

An electronic circuit that handles only a digital signal is called a digital circuit. The output voltage of a digital circuit is either low or high and no other value. In other words, digital operation is a two-state operation. These states are expressed as (High or Low) or (ON or OFF) or (1 or 0). Therefore, a digital circuit is one that expresses the values in digits 1’s or 0’s.Hence the name digital. The numbering concept that uses only the two digits 1 and 0 is the binary numbering system. Therefore, the first step would be to discuss this number system.

Number System

The study of number systems is important from the viewpoint of understanding how data are represented before they can be processed by any digital system including a digital computer. It is one of the most basic topics in digital electronics.

The number system that we use in day-to-day life is called Decimal Number System. In this system, one works with 10 different Digits, (0 through 9) and is known as based-ten system. But digital electronic devices used a 'strange' number system called binary. Digital computers and microprocessor -based systems use other strange number systems called Hexadecimal and Octal.

A number system is a method to represent (write) numbers. Every number system has a set of unique characters or literals. The count of these literals is called the radix or base of the number system. The four different number systems used in the context of computer.

Number systems are also called positional number system because the value of each symbol (i.e., digit and alphabet) in a number depends upon its position within the number. Number may also have a fractional part similar to decimal numbers used by us.

Number Systems

Decimal Number System

The decimal number system is used in our day-to-day life. It is known as base-10 system since 10 digits (0 to 9) are used. A number is presented by its two values — symbol value (any digit from 0 to 9) and positional value (in terms of base value).

The following shows the integer and fractional part of decimal number 237.25 alongwith computation of the decimal number using positional values.

Binary Number System

The ICs (Integrated Circuits) in a computer are made up of a large number of transistors which are activated by the electronic signals (low/high) they receive. The ON/ high and OFF/low state of a transistor is represented using the two digits 1 and 0, respectively. These two digits 1 and 0 form the binary number system.

This system is also referred as base-2 system as it has two digits only. Some examples of binary numbers are 1001011, 1011.101, 111111.01. A binary number can be mapped to an equivalent decimal number that can be easily understood by the human.

The decimal equivalent of the binary number 10101 (written as 10101)₂ is

1x2⁴ +0x2³ +1x2² +0x2¹ +1x2⁰ or 16+0+4+0+1 or 21

Thus, we write (10101)₂ = (21)₁₀

Octal Number System

With increase in the value of a decimal number, the number of bits (0/1) in its binary representation also increases. Sometimes, a binary number is so large that it becomes difficult to manage.

Octal number system was devised for compact representation of the binary numbers. Octal number system is called base-8 system as it has total eight digits (0-7), and positional value is expressed in powers of 8. Three binary digits (8=2³) are sufficient to represent any octal digit.

The decimal equivalent of the octal number 943 (written as 943)₈ is

9x8² +4x8¹ +3x8⁰ or

9x6⁴+32+3 or

576+32+3 or

611

so we have (943)₈ = (611)₁₀

Hexadecimal Number System

Hexadecimal numbers are also used for compact representation of binary numbers. It consists of 16 unique symbols (0 – 9, A–F), and is called base- 16 system.

In hexadecimal system, each alphanumeric digit is represented as a group of 4 binary digits because 4 bits (2⁴=16) are sufficient to represent 16 alphanumeric symbols. Note here that the decimal numbers 10 through 15 are represented by the letters A through F.

Examples of Hexadecimal numbers are (23A.05)₁₆, (1C3)₁₆, (619B.A)₁₆.

The decimal equivalent of the Hexadecimal number 3AF written as (3AF)16 or H

is 3x16² +Ax16¹ +Fx16⁰ or

3x256+10x16+15x1 or

768+160+15 or

943

Thus (3AF)₁₆ =(943)₁₀

Conversion between the Number Systems

Decimal to Binary

To convert decimal to binary, following steps are involved

Step 1: Divide the given number by 2.

Step 2: Note the quotient and remainder. Remainder should be 0 or 1.

Step 3: If quotient ≠ 0, then again divide the quotient by 2 and back to step 2. If quotient = 0, then stop the process.

Step 4: First remainder is called as Least Significant Bit (LSB) and last remainder is called as Most Significant Bit (MSB).

Step 5 Arrange all remainders from MSB to LSB.

Binary to Decimal

To convert binary to decimal, following steps are involved

Step 1 Multiply the all binary digits by powers of 2.

Step 2 The power for integral part will be positive and for fractional part will be negative.

Step 3 Add the all multiplying digits.

Binary to Octal

To convert binary to octal, following steps are involved

Step 1 Make the group of 3 bits from right to left. If the left most group has less than 3 bits, put in the necessary number of leading zeroes on the left.

Step 2 Now, convert each group to decimal number.

Octal to Binary

Convert every digit of the number from octal to binary in the group of 3 bits

Binary to Hexadecimal

To convert a binary number to its hexadecimal equivalent, follow these steps

Step 1 Start making the group of 4 bits each from right to left from the given binary number. If the left most group has less than 4 bits, put in the necessary number of leading 0’s on the left.

Step 2 Now, each group will be converted to decimal number.

Hexadecimal to Binary

For this type of conversion, convert each hexadecimal digit to 4 bits binary equivalent.

Decimal to Octal

To convert decimal to octal, following steps are involved

Step 1 Divide the given number by 8.

Step 2 Note the quotient and remainder. Digits of remainder will be from 0 to 7.

Step 3 If quotient ≠ 0, then again divide the quotient by 8 and go back to step 2.

Step 4 If quotient = 0 or less than 8 then stop the process.

Step 5 Write each remainder from left to right starting from MSD to LSD.

Octal to Decimal

To convert octal to decimal, following steps are involved

Step 1 Multiply each digit of octal number with powers of 8.

Step 2 These powers should be positive for integral part and negative for fractional part.

Step 3 Add the all multiplying digits.

Decimal to Hexadecimal

To convert decimal to hexadecimal, following steps are involved

Step 1 Divide the given number by 16.

Step 2 Note the quotient and remainder. Digits of remainder will be 0 to 9 or A to F.

Step 3 If quotient ≠ 0, then again divide the quotient by 16 and go back to step 2.

Step 4 If quotient = 0 or less than 16, then stop the process.

Step 5 Write each remainder from left to right starting from MSD to LSD.

Hexadecimal to Decimal

To convert hexadecimal to decimal, following steps are involved

Step 1 Multiply each digit of hexadecimal number with powers of 16.

Step 2 These powers should be positive for integral part and negative for fractional part.

Step 3 Add the all multiplying digits.

Octal to Hexadecimal

To convert octal to hexadecimal, following steps are involved

Step 1 Convert the each digit of octal number to binary number.

Step 2 Again, convert each binary digit to hexadecimal number.

Hexadecimal to Octal

To convert hexadecimal to octal, following steps are involved

Step 1 Convert the each digit of hexadecimal number to binary number.

Step 2 Again, convert each binary digit to octal number.

Computer Codes

In computer, any character like alphabet, digit or special character is represented by collection of 1’s and 0’s in a unique coded pattern. In computers, the code is made up of fixed size groups of binary positions. The binary coding schemes that are most commonly used are as follows

BCD

BCD stands for Binary Coded Decimal. This system was developed by IBM. It is a number system where four bits are used to represent each decimal digits. BCD is a method of using binary digits to represent the decimal digits (0-9). In BCD system, there is no limit on size of a number.

ASCII

ASCII stands for American Standard Code for Information Interchange. These are standard character codes used to store data so that it may be used by other software programs. Basically, ASCII codes are of two types which as follows

(i) ASCII-7 It is a 7-bit standard ASCII code. It allows 2⁷ = 128 (from 0 to 127) unique symbols or characters.

(ii) ASCII-8 It is an extended version of ASCII-7. It is an 8-bit code, allows 2⁸ = 256(0 to 255) unique symbols or characters.

EBCDIC

EBCDIC stands for Extended Binary Coded Decimal Interchange Code. In EBCDIC, characters are represented by eight bits. These codes store information which is readable by other computers. It allows 2⁸ = 256 combination of bits.

LOGIC GATES

Logic gates are the building blocks of digital electronics. The fundamental logic gates include the INVERT (NOT), AND, NAND, OR, NOR, exclusive OR (XOR), and exclusive NOR (XNOR) gates. Each of these gates performs a different logical operation.

Logic Gates The logic gate is the most basic building block of any digital system, including computers. Each one of the basic logic gates is a piece of hardware or an electronic circuit that can be used to implement some basic logic expression.

The three basic logic gates are the OR gate, the AND gate and the NOT gate

OR Gate

An OR gate performs an ORing operation on two or more than two logic variables. The OR operation on two independent logic variables A and B is written as Y = A+B and reads as Y equals A OR B and not as A plus B.

An OR gate is a logic circuit with two or more inputs and one output. The output of an OR gate is LOW only when all of its inputs are LOW. For all other possible input combinations, the output is HIGH.

The operation of a two-input OR gate is explained by the logic expression

Y = A+B

AND Gate

An AND gate is a logic circuit having two or more inputs and one output. The output of an AND gate is HIGH only when all of its inputs are in the HIGH state. In all other cases, the output is LOW.

The AND operation on two independent logic variables A and B is written as Y = A.B and reads as Y equals A AND B and not as A multiplied by B. Here, A and B are input logic variables and Y is the output. An AND gate performs an ANDing operation.

The operation of a two-input OR gate is explained by the logic expression

Y = A.B

NOT Gate

A NOT gate is a one-input, one-output logic circuit whose output is always the complement of the input. That is, a LOW input produces a HIGH output, and vice versa.

The NOT operation on a logic variable X is denoted as X or X . That is, if X is the input to a NOT circuit, then its output Y is given by Y = X’ and reads as Y equals NOT X. Thus, if X = 0 Y = 1 and if X = 1 Y = 0

NAND Gate

It is basically the inverse of the AND gate. This gate is designed by combining the AND and NOT gates. It returns False only if the both conditions or inputs are True otherwise it returns True.

NOR Gate

NOR stands for NOT OR. An OR gate followed by a NOT circuit makes it a NOR gate. The output of a NOR gate is a logic ‘1’ when all its inputs are logic ‘0’.

EXCLUSIVE-OR Gate

The EXCLUSIVE-OR gate, commonly written as EX-OR gate, is a two-input, one-output gate.

The output of a multiple-input EX-OR logic function is a logic ‘1’ when the number of 1s in the input sequence is odd and a logic ‘0’ when the number of 1s in the input sequence is even, including zero.

EXCLUSIVE-NOR Gate

EXCLUSIVE-NOR (commonly written as EX-NOR) means NOT of EX-OR, i.e. the logic gate that we get by complementing the output of an EX-OR gate.

The output of a multiple-input EX-NOR logic function is a logic ‘0’ when the number of 1s in the input sequence is odd and a logic ‘1’ when the number of 1s in the input sequence is even including zero. That is, an all 0s input sequence also produces a logic ‘1’ at the output.

Some Common Applications of Logic Gates

Initiation of protective action

Logic gates can be used in all those situations where the occurrence of any one or more than one event needs to be detected or acted upon. One such example is an industrial plant where any one or more than one parameter exceeding a preset limiting value should lead to initiation of some kind of protective action. Following figure shows a typical schematic where the OR gate is used to detect either temperature or pressure exceeding a preset threshold value and produce the necessary command signal for the system.

Controlling a LED with AND logic

Controlling a motor with AND logic

Controlling a relay with AND logic

A secreat code checker

How Boolean gates are made

Boolean gates can be made with Electric Switches and Transistors.

AND and OR functions with switches:

The Boolean operations AND and OR can be made with simple switches, as shown here:

Two switches connected in series will produce the AND function. Two switches connected in parallel will produce the OR function.

AND and OR functions with transistrors:

Digital Integrated Circuits

An integrated circuit

(IC) contains multiple components on a single piece of silicon in a package that has external electrical contact points, or pins. ICs are also known as chips.

Generally we use dual in- line package (DIP) IC package, a rectangular enclosure with two parallel rows of pins. These pins are spaced so they can easily be used on a breadboard.

SN7432N integrated circuit in a dual in- line package

The logic circuits we discussed earlier that used resistors and transistors are known as resistor–transistor logic (RTL) circuits. Manufacturers built early digital logic circuits this way, but later they used other approaches, including diode–transistor logic (DTL), and transistor–transistor logic (TTL). The 7400 series is the most popular line of TTL logic circuits.

The logic families that use MOS (Metal Oxide Semiconductor) devices as their basis are known as MOS families, and the prominent members belonging to this category are the PMOS family (using P-channel MOSFETs), the NMOS family (using N-channel MOSFETs) and the CMOS family (using both N- and P-channel devices).

Let's examine a specific 7400 series integrated circuit. The 7432 chip, shown in the following Figure, contains four OR gates.

A pinout diagram of 7432

Pinout diagram—a diagram that labels the electrical contacts, or pins, of a component. The purpose of such a diagram is to show the component’s external connection points, but usually a pinout diagram does not document the internal design of the circuit.

The 7432 IC comes in a package with 14 pins. Each of the four OR gates requires 3 pins, so that’s 12 pins, plus 1 pin for positive voltage (Vcc) and 1 pin for ground, giving us 14 pins in total. Speaking of voltage, the 7400 series operates with an expected Vcc of 5V. That is, high voltage, a logical 1, is ideally 5V, and low voltage is 0V. However, in practice an input voltage of anywhere between 2V and 5V registers as high, and anywhere between 0V and 0.8V is considered low.

Pin configuration of Commonly used Digital ICs

Construction of a logic circuit with ICs

Logic Diagram

Wiring diagram for (A+B).C

Boolean algebra

To perform the logical operation with minimum logic gates, a set of rules were invented, known as the Laws of Boolean Algebra. These rules are used to reduce the number of logic gates for performing logic operations.

The Boolean algebra is mainly used for simplifying and analyzing the complex Boolean expression. It is also known as Binary algebra because we only use binary numbers in this. George Boole developed the binary algebra in 1854.

Rules in Boolean algebra

1. Only two values(1 for high and 0 for low) are possible for the variable used in Boolean algebra.

2. The overbar(-) is used for representing the complement variable.

3. The plus(+) operator is used to represent the ORing of the variables.

4. The dot(.) operator is used to represent the ANDing of the variables.

5. The equals (=) sign in Boolean algebra refers to the standard mathematical equality. In other words, the logical value on one side of the sign is identical to the logical value on the other side of the sign. Suppose we are given two logical variables such that A = B. Then if A = 1, then B = 1 and if A = 0, then B = 0.

Few Properties of Boolean algebra:

AA = A

A + A = A

A + A =1

AA' =0

(A')'= A

A+0 = A

A+1 = 1

A.0 = 0

A.1= A

A+B = B+A

A.B = B.A

De Morgan’s Theorems:

De Morgan’s theorems are extremely useful in simplifying expressions in which a product or sum of variables is inverted.

The two theorems are :

(i) ( A+ B)’ = A’.B’

(ii) (A B)’ = A’ + B’

The first De Morgan’s theorem may be stated as under : When the OR sum of two variables is inverted, this is equal to inverting each variable individually and then ANDing these inverted variables i.e., ( A+ B)’ = A’.B’

In this expression, A and B are the two variables. The L.H.S. is the complement of the OR sum of the two variables. The R.H.S. is the AND product of individual inverted variables.

The second De Morgan’s theorem may be stated as under: When the AND product of two variables is inverted, this is equal to inverting each variable individually and then ORing them i.e., (A B)’ = A’ + B’ In this expression, A and B are the two variables. The L.H.S. is the complement of the AND product of the two variables. The R.H.S. is the OR sum of the individual inverted variables

Operator Precedence:

The operator precedence for evaluating Boolean expression is (i) parenthesis (ii) NOT (iii) AND and (iv) OR.

In other words, the expression inside the parenthesis must be evaluated before all other operations. The next operation that holds precedence is the complement, then follows the AND and finally the OR.

For example, consider the Boolean expression :

A + B'.(C+ D )

The sequence of operations will be :

(i) The expression inside the parenthesis (i.e. C + D) will be evaluated first.

(ii) Then B will be evaluated.

(iii) Then the results of the two (i.e. B and C + D) will be ANDed.

(iv) Finally, the result of the product will be ORed with A.

Truth tables

A truth table is a table of the value of a Boolean expression for all possible values of the inputs. For example, this is a table for the expression F = A * (B+C).

Sometimes, you want to build a digital circuit with a given functionality that is defined only by a truth table. You can use the so-called sum-of-products method to find a Boolean expression that corresponds to a given truth table. This method works as follows:

Find all the lines in the truth table for which the output is 1. Make one expression for each of these lines by AND'ing all the inputs and inverting those inputs that are 0 in that line. Each of these expressions is 1 in the corresponding line and 0 in the rest. The final result is the OR-combination of all these expressions. Let's try this method with the example above.

Now we know that F = A*B̅*C + A*B*C̅+ A*B*C.

This is called a sum of products, even though the * and + actually mean AND and OR.

Now we have a valid expression for F, but not the simplest possible one. We may simplify this expression by using the laws and rules that we have learnt:

A*B̅*C + A*B*C̅+ A*B*C =

A*B̅*C + A*B*(C̅+ C) =

A*B̅*C + A*B*1 =

A*B̅*C + A*B =

A * (B̅*C + B) =

A * (B + B̅*C) =

A * (B + C)

If there are many 1's and few 0's in the output column, then it is easier to invert the output and apply the sum-of-products method to the inverted output. This gives a simpler expression, but we must remember to invert the result of the expression. We can use de Morgan's rule for converting the inverted sum of products to a "product of sums".

Logical Systems

The logic gates produce a fixed output for every combination of inputs. Each gate has a truth table that describes its action. We can connect several gates together in a logical circuit and write a truth table that describes the outputs for every combination of inputs. This is called combinational logic.

A combinational logic circuit is one where the output or outputs depend upon the present state of combination of the logic inputs.

Designing Circuits

The different steps involved in the design of a combinational logic circuit are as follows:

1. Statement of the problem.

2. Identification of input and output variables.

3. Expressing the relationship between the input and output variables.

4. Construction of a truth table to meet input–output requirements.

5. Writing Boolean expressions for various output variables in terms of input variables.

6. Minimization of Boolean expressions.

7. Implementation of minimized Boolean expressions.

Examples: Designing Circuits

Sprinkler Control

A system is designed to turn on a garden water sprinkler when the soil is dry, but not when the sun is shining. A light sensor A has outputs 0=dull, and 1=sunny. A soil moisture sensor B has outputs 0=moist, and 1=dry. For the sprinkler S, 0=off, and 1=on. The truth table for the system is:

The logic equation for the output S is A'B.

S + A'B

The logic diagram for A'B is:

Half Adder

A half-adder is an arithmetic circuit block that can be used to add two bits. Such a circuit thus has two inputs that represent the two bits to be added and two outputs, with one producing the SUM output and the other producing the CARRY.

The truth table of a half-adder

The Boolean expressions for the SUM and CARRY outputs are given by the equations

SUM S = A'.B +A.B'

CARRY C = A.B

An examination of the two expressions tells that there is no scope for further simplification. While the first one representing the SUM output is that of an EX-OR gate, the second one representing the CARRY output is that of an AND gate.

Sequential Logic circuits

The output depends only on the inputs on digital circuits that have no memory. Such a circuit is called combinational because the output is a combination of the inputs. The circuits we have seen in the previous chapters were all combinational.

The output may depend not only on the inputs, but also on the past history, on circuits that contain memory elements. Such a circuit is called sequential because the output depends on a sequence of inputs. Now we will see how to create memory elements so that we can construct sequential logic circuits.

The flip-flop is an important element of such circuits. It has the interesting property of memory: It can be set to a state which is retained until explicitly reset.

SR flip-flop

The circuit above is not very useful because we cannot change the state. Now we will replace the inverters by NOR gates so that we can change the state. The input S is used for setting Q high. The input R is used for resetting Q to low.

We have the same feedback as before as long as the two inputs S and R are both low. Either Q will be low and Q̅ will be high, or Q will be high and Q̅ will be low. We can force Q̅ to be low by setting S high because the output of a NOR gate is always low when at least one of the inputs is high. We assume that R is still low, so Q will be high. In other words, we can change the circuit to the state where Q is high by setting S high and low again. The opposite happens when we set R high and low again. This will make Q low and Q̅ high.

This circuit is called an SR flip-flop. The S stands for set, and R stands for reset. We can write the truth table:

Debounced Switch using NAND gates

A useful example of the simple SR flip-flop is the debounced switch.Any simple mechanical switch will bounce as it makes contact. Hence, an attempt to provide a simple transition from digital HIGH to LOW with a mechanical switch may result in an unintended series of transitions between the two states as the switch damps to its final position.

Building Blocks of Digital circuits

Half adder

Full adder

A full adder circuit is an arithmetic circuit block that can be used to add three bits to produce a SUM and a CARRY output.

Half-Subtractor

A half-subtractor is a combinational circuit that can be used to subtract one binary digit from another to produce a DIFFERENCE output and a BORROW output. The BORROW output here specifies whether a ‘1’ has been borrowed to perform the subtraction.

Four-bit binary adder

The full adder of the type described above forms the basic building block of binary adders. However, a single full adder circuit can be used to add one-bit binary numbers only. A cascade arrangement of these adders can be used to construct adders capable of adding binary numbers with a larger number of bits.

Parity Tree

Parity trees are used for checking if a byte of data is correct. In an 8-bit system, 7 bits are reserved for the data and the eighth bit is the parity bit. When the data is prepared, the numbers of 1’s in each group of 7 bits is counted. The parity bit is then made 0 or 1, so as to make the total number of 1’s odd. This is called odd parity. Later, perhaps after having been transmitted and received elsewhere, the data can be checked by feeding it to a parity tree.

If the data is correct it still has odd parity and the output of the tree goes high. If one of the bits has changed, the number of 1’s is even and the output of the tree goes low, warning that the data is corrupted.

MAGNITUDE COMPARATOR

This circuit compares two 4-bit words, and gives a low output if they are identical. The two inputs of each gate receive the corresponding bit from each word.

DECIMAL TO BINARY CONVERTER

Assuming that only one input is high at any one time, the circuit in Figure 20.7 produces the 2-bit binary equivalent of the decimal numbers 1 to 3. An extended converter is built with three 3-input OR gates to convert numbers from 1 to 7. A circuit that converts decimal to binary is also called an encoder, which is sometimes shortened to coder.

BINARY TO DECIMAL CONVERTER

This performs the reverse function to the previous circuit. Given a binary input, the one corresponding decimal output goes high. A circuit such as this, which converts binary to decimal, is also known as a decoder.

DATA SELECTOR

A data selector (or multiplexer) has several inputs but only one or two outputs. The data selector circuit below has two inputs, A and B, and one output, Z.

The action of the selector depends on the logic level at the select input, S. If S is low, as in the figure, output Z follows the state of input A. Conversely, Z follows B if S is high. So, by setting S to 0 or 1, we can select data A or data B. The select input is the equivalent of an address, the two possible addresses in this circuit being 0 or 1.

4:1 MUX

DATA DISTRIBUTOR

This performs the opposite function to a data selector, and is often called a demultiplexer. It has one data input and the data may be routed to any one of several outputs. There are address inputs to select which output is to show the data.

1:4 DEMUX

Commonly used IC type numbers used for arithmetic operations.

Arithmetic Logic Unit (ALU)

The arithmetic logic unit (ALU) is a digital building block capable of performing both arithmetic as well as logic operations. Arithmetic logic units that can perform a variety of arithmetic operations such as addition, subtraction, etc., and logic functions such as ANDing, ORing, EX-ORing, etc., on two four-bit numbers are usually available in IC form. The function to be performed is selectable from function select pins. Some of the popular type numbers of ALU include 74181, 74381, 74382, 74582 (all from the TTL logic family) and 40181 (from the CMOS logic family).

Single Bit ALU

The circuit functionality of a 1 bit ALU is shown here, depending upon the control signal S1 and S0 the circuit operates as follows:

for Control signal S1 = 0 , S0 = 0, the output is A And B,

for Control signal S1 = 0 , S0 = 1, the output is A Or B,

for Control signal S1 = 1 , S0 = 0, the output is A Xor B,

for Control signal S1 = 1 , S0 = 1, the output is A Add B.