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Engistan.com [Digital Electronics for IBPS IT-Officer 2014]

Digital circuit: Circuit in which the signal used can have fixed number of discrete states. It consists of logic gates, electronic devices. Mobile phone, digital watch, calculators, computers, video games etc are example of digital circuits.

Advantages of digital circuits:

• Less susceptible to noise or degradation in quality than analog circuits. • Easy to perform error detection and correction with digital signals.

Digital logic:

• It shows the communication between circuits and hardware within a computer. • It is representation of signals and sequences of a digital circuit through numbers. • Digital logic is typically embedded in most electronic devices.

Digital Signal/ Logic signal: It is a physical signal which is used for representation of a sequence of discrete values. They can be represented as:

• Truth values:- true (T) and false (F) • Boolean values:-1 and 0. • Voltage:- represented as “high” (H) or “low” (L) • For switch:- on/off OR open/close etc

Operations on Logic Signals:

A and B two signals are input set for a given circuit and produces a output signal C, which depends on A and B.

C can be result of AND, OR ,NOT, NAND, NOR, XOR function between A and B.

Logic gates: These are use to perform logic operations on logical inputs and produces a single logical output. If A is a digital signals then A could be either TRUE (a logical 1) or FALSE (a logical 0).

• And Gate: The output of AND gate is TRUE only if both the inputs to the AND gate is TRUE. Truth table for And gate:

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Input Output A B C False False False False True False True False False True True True

Symbol for And gate:

Also C= A.B

• OR gate: The output of or gate is true if one or both the inputs to the gate are true (1). Truth table for OR gate:

Symbol for OR gate:

Also C=A+B

• Not gate: It represents negation i.e false for true and true for false. If A is input signal and B is output t signal then Truth table for Not gate:

Input Output A B 0 1 1 0

Symbol for Not gate:

Input Output A B C False False False False True True True False True True True True


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Also B=~A

• Nand gate: It is an AND gate with an inverter on the output

Input Output A B C 0 0 1 0 1 1 1 0 1 1 1 0

Symbol for Nand gate:

Also C= . or

• NOR gate: It is an OR gate with an inverter on the output.

Input Output

A B C

0 0 1

0 1 0

1 0 0

1 1 0

Symbol for NoR gate:


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Also C= or

• XOR gate: It is used as an exclusive or. The output is true if one, and only one, of the inputs to the gate is true.

Input Output

A B C

0 0 0

0 1 1

1 0 1

1 1 0

Also C= = A’B+B’A

• XNOR gate: It is inverse of XOR. The output is high if both of the inputs to the gate are the same.

Input Output

A B C

0 0 1

0 1 0


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http://en.wikipedia.org/wiki/File:XOR_ANSI.svg

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1 0 0

1 1 1

Also C= or = A’B’+ AB

Note: NOR gates alone or alternatively NAND gates alone can be used to reproduce the functions of all the other logic gates so they are called Universal gates.

Number system:

In digital logic number can be represented in various forms:

Number System Base Representation of numbers is using

Binary number 2 0 (zero) and 1 (one)

Decimal numbers 10 0 to 9

Octal numbers 8 0 to 7

Hexadecimal 16 0 to 9 digits and A to Z alphabets

Complements: They are used in digital computer for simplifying the subtraction operation and for logic manipulation.

Codes in digital logic:

Binary Codes: In such case signal will have 2 values (0/1) and circuit elements will have two stable states.

Note:- A Bit is a binary digit.


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Decimal Codes: Binary codes for decimal number require a minimum of 4 bits. There are 5 type of decimal codes:

• BCD • Excess-3 • 84-2-1 • 2421

Error detection code: value of parity bit is used for error detection

Reflected Code: In such code only 1 bit changes as we proceed from 1 number to another.

Alphanumeric code: This code consist 10 decimal digits and 26 letter of alphabets.

Boolean Laws:

T1 : Commutative Law (a) A + B = B + A (b) A B = B A

T2 : Associate Law (a) (A + B) + C = A + (B + C) (b) (A B) C = A (B C)

T3 : Distributive Law (a) A (B + C) = A B + A C (b) A + (B C) = (A + B) (A + C)

T4 : Identity Law (a) A + A = A (b) A A = A

T5 : (a) (b)

T6 : Redundance Law (a) A + A B = A (b) A (A + B) = A

T7 : (a) 0 + A = A (b) 0 A = 0

T8 : (a) 1 + A = 1 (b) 1 A = A

T9 :

(a)

(b) T10 :

(a)

(b)


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T11 : De Morgan's Theorem

(a)

(b)

Methods to solve Boolean expression:

Boolean algebra: area of mathematics using which Boolean expression are solved.

Karnaugh map (K map): A Karnaugh Map is a grid-like representation of a truth table. A Karnaugh map has zero and one entries at different positions. Each position in a grid corresponds to a truth table entry.

For example:

A B C V 0 0 0 0 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 1

Logic circuits are of two types:

• Combinational: It consists of logic gates whose outputs at any time are determined directly from the present input without regards to previous inputs.


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• Sequential: it consists of memory elements in addition to logic gates. Their output is

function of input and the state of the memory elements. And this is function of previous input.

BLOCK DIAGRAM

Examples of combinational circuits:

Adders: These are used for addition of bits. There are two type of adder:

Half adder: This circuit consists of two binary inputs (two bits that used need to add) and two binary outputs (sum and carry).

Block digram:


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TRUTH TABLE

CIRCUIT DIAGRAM

Full Adder: It takes three inputs (two bits that user need to add plus one carry bit) and produces two outputs(sum and carry).

BLOCK DIAGRAM

TRUTH TABLE


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CIRCUIT DIAGRAM

Substractor: These are used for substraction of bits. There are two type of substractor:

Half Substractor: This circuit consists of two binary inputs (two bits that used need to substract) and two binary outputs (difference and borrow).

TRUTH TABLE


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CIRCUIT DIAGRAM

Full Substracor: This circuit consists of three binary inputs (two bits that used need to substract and one borrow) and two binary outputs (difference and borrow).

TRUTH TABLE

CIRCUIT DIAGRAM


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Binary parallel Adder: It produces arithmetic sum of 2 binary numbers in parallel. It consists of full adder connected in cascade. It work on the carry propagation concept.

BLOCK DIAGRAM

Decimal adder: It need minimum of 9 inputs in decimal form and produces 5 outputs of BCD form.

BCD Adder: used to add two BCD digits and produces a sum digit also in BCD.

Magnitude Comparator: Used to compare two numbers

Decoder: Converts binary information from n inputs to a max of 2^n unique information. For example:

• Code converters • BCD to seven segment decoders • Nixie tube decoders


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• Relay actuator

BLOCK DIAGRAM

Demultiplexers: A decoder with enable function is demux. It receive information on a signal line transmit this information on one of 2^n possible output lines. The selection of output is controlled by bit values of n selection lines.For example:

• 1 : 2 demultiplexer • 1 : 4 demultiplexer • 1 : 16 demultiplexer • 1 : 32 demultiplexer

• BLOCK DIAGRAM

• • TRUTH TABLE

•

Encoders: it produces a reverse operation from that of a decoder. An encoder has 2^n or less input lines and n output lines. For example:

• Priority encoders • Decimal to BCD encoder


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• Octal to binary encoder • Hexadecimal to binary encoder

BLOCK DIAGRAM

Multiplexers: It selects binary information from one of the many input lines(max 2^n) and directs it to a single output line. It has n select lines whose combination determine which input is seleted. For example:

• 2 : 1 multiplexer • 4 : 1 multiplexer • 16 : 1 multiplexer • 32 : 1 multiplexer

BLOCK DIAGRAM

BLOCK DIAGRAM


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TRUTH TABLE

Sequential circuits:

Basic Flip Flop circuits: a flip-flop or latch is a circuit that has two stable states and used to store state information. It is also called bistable multivibrator. The circuit can have one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. It is constructed from 2 nand and 2 nor gates.

Type of flip flop:

Clocked RS flip flop: Basic flip flop plus clock is Clocked RS flip flop.

BLOCK DIAGRAM

CIRCUIT DIAGRAM


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TRUTH TABLE

D flip flop: It is an RS flip flop with an inverted in the R input.

BLOCK DIAGRAM

CIRCUIT DIAGRAM


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TRUTH TABLE

JK flip flop: It is refinement of RS flip flop. It is same as SR flip flop but contain feedback from the output of second to input of first.

TRUTH TABLE

T flip flop: It is an JK flip flop with an inverted in the K input.

SYMBOL DIAGRAM

BLOCK DIAGRAM


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TRUTH TABLE

Registers: It is a group of binary storage cell (flip flop) suitable for holding binary information.

Shift registers: Store binary information either to left or right. There are four mode of opearation of a shift register.

• Serial Input Serial Output • Serial Input Parallel Output • Parallel Input 0053erial Output • Parallel Input Parallel Output

Counters: counter is a device which is used to count number of times a particular event or process has occurred. There are 2 type of counters:

• Rippel counter • Synchronous counter

Ripple counter: the flip flop output transition serves a source for triggering other flip flop.

LOGICAL DIAGRAM


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Type of ripple counter:

• binary ripple counter • BCD ripple counter

Synchronous counter: The input pulse are applied to all the clock pulse input of flip flops.

2-BIT SYNCHRONOUS UP COUNTER The JA and KA inputs of FF-A are tied to logic 1. So FF-A will work as a toggle flip-flop. The JB and KBinputs are connected to QA.

LOGICAL DIAGRAM

Type of Synchronous counter:

• Binary Synchronous counter. • Binary up down counter • BCD Counter

Classification of counters

Depending on the way in which the counting progresses, the synchronous or asynchronous counters are classified as follows:-

• Up counters • Down counters • Up/Down counters

Modulus Counter (MOD-N Counter):

The 2-bit ripple counter is called as MOD-4 counter and 3-bit ripple counter is called as MOD-8 counter. So in general, an n-bit ripple counter is called as modulo-N counter. Where,MOD number = 2^n

TYPE OF MODULUS:


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• 2-bit up or down (MOD-4) • 3-bit up or down (MOD-8) • 4-bit up or down (MOD-16)

Application of the counters:

• Frequency counters • Digital clock • Time measurement • A to D converter • Frequency divider circuits • Digital triangular wave generator


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