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

    Also C= or

    XOR gate: Itis 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= = AB+BA

    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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    1 0 0

    1 1 1

    Also C= or = AB+ 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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    Engistan.com [Digital Electronics for IBPS IT-Officer 2014]

    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 = 0T8 :

    (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:Itconsists 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 JAand KA inputs of FF-A are tied to logic 1. So FF-A will work as a toggle flip-flop. The JBand

    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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