Digital Circuits

 What is Number System?

The Number system used in digital circuits is binary, which is based on the power of 2 & uses the digits 0 & 1.

There are two types of number system.

1. Positional number system

2. Non-Positional number system

1. Positional Number System:- 

       There are only a few symbols called digits. These symbols represent different values depending on the position they occupy in a number. The value of each digit in such a number is determine by three considerations.

1. The digit it self

2. The position of the digit in the number.

3. The base of the number system (Where base is defined as the total number of digits available in the number system.)

2. Non-Positional Number system:-

     Each symbol represents the same value regardless of its position in the number & to find the value of a number, one has to count the number of symbols present in the number. It is very difficult to perform arithmetic with such a number system.

Some Types of Positional number system

1. Binary Number System

2. Octal Number System

3. Hexa-decimal Number System

4. Decimal Number System

a.) Binary Number System:- Its value of base 2. It has only two symbols or digits (0 & 1). Each position in a binary number represents a power of the base (2).

        Example:-             ( 1 0 1 0 1 )2

    (1x24)+(0x23)+(1x22)+(0x21)+(1x20) = 16+0+0+1 = (21)10

Binary	Decimal	Hexa-Decimal
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
0111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F

20       21       22       23       24       25         26

1         2        4        8        16      32       64

b.) Octal Number System:- Its value of base 8. There are only eight symbols or digit: 0,1,2,3,4,5,6 & 7. Each position in an octal number represents a power of the base (8).

Example :         (2057)8

                       (2x83)+(0x82)+(5x81)+(7x80) = 1024+0+40+7 = (1071)10

c.) Hexa-Decimal Number System :- Its value of base is 16. There are 16 symbols or digits. The first ten digits are the same digits of decimal number system - 0,1,2,3,4,5,6,7,8 & 9. The ramining 6 digits are the symbols A,B,C,D,E & F representing decimal values 10, 11 , 12, 13, 14 & 15 respectively.

Each position in hexadecimal number system represents a power of the base (16).

Example :- (1AF)16

(1x162)+(Ax161)+(Fx160) = 256+160+15 = (431)10

d.) Decimal Number System:- Its value of base 10. There are ten symbols or digits (0,1,2,3,4,5,6,7,8 & 9). Each position represents a specific power of the base (10). 

For Example :-          (2586)10

 (2x103)+(5x102)+(8x101)+(6x100) = 2000+500+80+6 = (2586)10

Convert Binary to decimal

1. Convert the binary number (1101)2 in to a Decimal Number?

              Conversion = (1101)2  = (?)10

Step 1 =     1    1    0    1

Step 2 =    23   22   21   20

Step 3 =    8    4    2     1

Step 4 =    (Step 1 * Step 3) = (1  1  0  1 * 8  4  2  1 )

Step 5 =    8+4+0+1 = (13)10

2. Convert the binary number (1001)2 in to a Decimal Number?

Conversion = (1001)2  = (?)10

Step 1 =     1    0    0    1

Step 2 =    23   22   21   20

Step 3 =    8    4    2     1

Step 4 =    (Step 1 * Step 3) = (1  0  0  1 * 8  4  2  1 )

Step 5 =    8+0+0+1 = (9)10

Convert Decimal to Binary

1. Convert the decimal number (9)10 in to a binary Number?

              Conversion = (9)10  = (?)2

Step 1 =     23   22   21   20

Step 2 =     8    4    2     1

Step 3 =     1    0    0     1

Step 4 =       (1001)2

2. Convert the decimal number (14)10 in to a binary Number?

              Conversion = (14)10  = (?)2

Step 1 =     23   22   21   20

Step 2 =     8    4    2     1

Step 3 =     1    1    1     0

Step 4 =       (1110)2

Convert Octal to Binary

Note :- Pairs of 3-3 are made in octal.

1. Convert the octal number (632)8 in to a binary Number?

              Conversion = (632)8  = (?)2

Step 1 =  6 = 4   2   1=  1  1  0

Step 2 =  3 = 4   2   1=  0  1  1 

Step 3 =  3 = 4   2   1=  1  0  1   

Step 4 =       (110 011 101)2

2. Convert the octal number (537)8 in to a binary Number?

              Conversion = (632)8  = (?)2

Step 1 =  5 = 4   2   1=  1  0  1

Step 2 =  3 = 4   2   1=  0  1  1 

Step 3 =  7 = 4   2   1=  1  1  1   

Step 4 =       (101 011 111)2

Convert Binary to Octal

1. Convert the binary number (111)2 in to a octal Number?

              Conversion = (111)2  = (?)8

Step 1 =  1  1  0

Step 2 =  4  2   1 

Step 3 =  4+2+1  

Step 4 =       (7)8

2. Convert the binary number (1010101)2 in to a octal Number?

              Conversion = (1 010 101)2  = (?)8

Step 1 =        1 = 1

Step 2 =  0 1 0 = 2 

Step 3 =  1 0 1 = 5  

Step 4 =       (125)8

Convert Binary to Hexa-Decimal

Note :- Pairs of 4-4 are made in Hexa-Decimal.

1. Convert the binary number (1000)2 in to a Hexa-Decimal Number?

              Conversion = (1000)2  = (?)16

Step 1 =  1  0  0  0

Step 2 =  8  4  2 1 

Step 3 =  (7)16  

   

2. Convert the binary number (1010101101001)2 in to a Hexa-Decimal Number?

              Conversion = ( 1 0101 0110 1001 )2  = (?)16

Step 1 =  1 = 1 

Step 2 =  0101 = 5 

Step 3 =  0110 = 6

Step 4 =  1001 = 9

Step 5 =  (1569)16

 

Convert Hexa-Decimal to Binary

1. Convert the hexadecimal number (5AD)16 in to a binary Number?

              Conversion = (5AD)16  = (?)2

Step 1 =  5 =  0  1  0  1

Step 2 =  A = 10 = 1  0  1  0 

Step 3 =  D = 13 = 1  1  0  1

Step 3 =  (0101 1010 1101)2

Convert Octal number to Hexadecimal number

                 (26)8  = (?)16  

                  (26)8  = (?)2

                    2 = 0  1  0

                    6 = 1  1  0

              (26)8  = (010 110)2

               (010 110)2  =   (?)16  

        (0010 0110)2  =   (?)16 

             (16)16

Convert Hexadecimal number to Octal number.?

                 (AE)16  = (?)8

                 (AE)16  = (1010 1110)2

             (AE)16  = ( 010 101 110 )2

                 (AE)16  = (256)8

BCD CODE:- 

BCD CODE is one of the early computer codes.Each digit of a decimal number is represented by its binary equivalent instead of converting the entire decimal value to a binary number.This makes the conversion process easier.

Decimal Digits	BCD Equivelent
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001

 Note :- Each Decimal digit is converted independently to a 4 bit binary number. The conversion process is very easy. When 4 bits are used 24 = 16 combination are possible.(Refer to hexadecimal number system). The remaining six arrangements (1010, 1011, 1100, 1101, 1110 & 1111) have decimal values from 10 to 15. BCD coding does not use these arrangement. I.e. 1010 does not represent (10)10 in BCD.

Example :- (10)10  =  0001     0000  or 00010000 in BCD

                                    1           0

                   (15)10  =  0001    0101  or   00010101 in BCD

                                     1           5     

Logic Gates :-

Logic Gates are basic building blocks of any digital system. It is an electronic circuit having one or more than one input and only one output.

The relationship b/w input & output is based on a certain logic, Which is named as boolean expression, such as AND, OR & NOT. These three gates are called basic gates.

AND Gate :- If all inputs are 1, Then output is 1. Otherwise, The output is 0 or if any input is 0, output is 0. AND is denoted by a dot(.)

Bollean Expression :-

                                    Y = A.B

OR Gate:- If all input are 0, The output is 0. Otherwise, The output is 1 or if any input is 1, output will be 1, OR is denoted by a plus (+).

Boolean Expression :-

                                            Y = A+B

NOT Gate :- A NOT gate accepts one input signal (0 or 1) and returns the opposite signal as output. NOT is denoted by an over bar (-), a singal quote mark (').

Boolean Expression :-         

                                                            Y = A'

Universal Gate :- Any logic gate or logic function can be realized using this logic gate.

There are two types of Universal logic gates:-

        1. NAND Gates                 2. NOR Gates

NAND Gate:- If all inputs are 1, the output is 0, Otherwise, The output is 1.

                                                        Y = (A.B)'

                    

                                              NAND = AND + NOT

NOR Gate :- If all inputs are 0, the o/p is 1, other, The output is 0.

            

                                                   NOR= OR + NOT

Boolean Expression :-

                            Y = (A+B)'

Other Logic Gates

X OR Gate:- If odd numbers of input are 1, The output is 1, Otherwise The output is 0.

Boolean Expression:-

                                                 Y = A B' + A'B

X NOR Gate :- The output of the XNOR Gate is logic 1. When both the inputs are logic 1, or logic 0. This logic gate is denoted by this sign 'o'.

                        Boolean Expression

                                                Y = AB + A'B'

                                EX-NOR = EX-OR + NOT

Demorgan's Theorem :-

Demorgan's theorem are basically two sets of rules or laws developrd from the boolean expressions for AND OR & NOT using two input variablrs A & B.

These two rules or theorems allow the input variables to be nigated and converted from one from of a boolean function in to an opposite form.

Theorem First :- The first theorem of Demorgan's law defines that the inverted result from AND operation is the same as the OR operation of the complement of each variable.

Theorem Second :- The second Theorem of Demorgan's law define that the inverted result from OR operation is the same as the AND operation of the complement of each variable.

Boolean Algebra :- Boolean Algebra is a branch of Algebra (Mathematics) that deals with operations on logical values with boolean variables. boolean variables are represented as binary numbers which takes logic 1 and logic 0 values. Hence, The Boolean Algebra is also called two-valued logic, Binary Algebra or Logical Algebra. The boolean Algebra was introduced by great mathematiciuan George Bool in 1847. The Boolean Algebra is a fundamental for the development of digital electronics system, and is provided for the representation, simplification and analysis of mathematical quantities.

Logic level are classified into two types :-

1. Positive Logic

Logic 0 = False, 0V, Open Switch, OFF

                            Logic 1 = True, +5V, Closed

2. Negative Logic

                            Logic 0 = True, +5V, Closed Switch, ON

                            Logic 1 = False, 0V, Open Switch, OFF

Boolean algebra differs from normal or elementary algebra. Latter deals with numerical operations such as addition, subtraction, multiplication & division on decimal numbers. And former deals with the logical operations such as conjuction (OR), DISJUNCTION (and) & negation (NOT).

                    In present context, positive logic has been used for the entire discussion, represetation and simplification of Boolean Variables.

Boolean Laws:-

1. Commutative Law :- The sequence of changing the variables does not effect on the result even after changing their sequence while performing OR/AND operations of Boolean expression.

                                      A.B = B.A & A+B = B+A

2. Associative law:- The order of oprations on variables is independent.

                         A.(B.C) = (A.B).C & A+(B+C) = (A+B)+C

3. Distributive laws:-

                                A.(B+C) = A.B+A.C

                                A+BC = (A+B)(A+C)

4. AND Laws :-

                                A.0 = 0

                               A.1 = A

                               A.A = A

                               A.A' =0

5. OR Laws :-

                                A+0 = A

                               A+1 = 1

                               A=A = A

                               A+A' = 1

6. Inversion/Complement/NOT Laws:-

                                 0' = 1

                                1' = 0

                                A' = A

7. Absorption Laws :-

                                 A(A+B) = A

                                A+AB = A

                                A+A'B = A+B

Q. Realize the following boolean expression using basic gates.

            Y = AB+BC+AC

Ans :- Logic Diagram

     

    Q. Simplify the following expressions?

            Y= BC+BC'+BA

Ans:-

             Y = BC+BC'+BA

             Y = B(C+C')+BA

             Y = B+BA             (C+C' = 1)

             Y = B(1+A)           (1+A = 1)

             Y = B.1

             Y = B

Q.- Y = C+B'C'

Ans:-

              Y = C+B'C'

              Y = C+B'+C'

              Y = (C+C')+B'

              Y = 1+B'

             Y = 1

Maxterm & Minterm

A minterm is a Boolean AND function containing exactly one instant of each input variable or its inverse. It is denoted by m.

Such as m1, m2, m3 etc. It is a SOP form.

   F(A,B,C) = A’BC+AB’C+ABC’ (SOP)

A Maxterm is Boolean OR function with exactly one instant of each variable or its inverse. It is denoted by M. Such as M0, M2. It is POS form.

F(A,B,C) = (A’+B+C).(A’+B+C’).(A’+B’+C).

Product of sum (POS):- A canonical product of sum is a boolean expression

that entirely consists of maxterm. When function F = 0,

Then A = 0, A’ = 1.

Maxterm	A	B	F
M0	0	0	0
M1	0	1	1
M2	1	0	0
M3	1	1	1

F(A,B) = (A+B).(A’+B)

F = ЛM (M0, M2)

F(A,B) =  ЛM (0,2)

Sum of Product:- A Canonical sum of product is a boolean expression that entirely consists of Minterm. When function F = 1, Then A = 1, A’ = 0.

F(A,B) = A’B+ AB’ + AB                             F = Ʃm (m₁,m₂,m₃)             

F(A,B) = Ʃm (1,2,3)

Minterm	A	B	F
m0	0	0	0
m1	0	1	1
m2	1	0	1
m3	1	1	1

To make canonical standard SOP form :- Multiply by (A+A’) term of missing variable.

e.g. A’+B’ = A’(B+B’) + B(A+A’)

To make canonical standard POS form:- Add (A.A’) term of missing variable.

 E.g. A’(B+C) = (A’+B.B’+C.C’).(B+C+A.A’)

K-MAP (Karnaugh map):- 

K-Map refers to a pictorial method that is utilised to

systematic way of simplifying Boolean Expression.

We can find all simplest POS & SOP expression.

Step to create K-map & simplifying Boolean Expression.

STEP1:- We find the K-map as per the number of variables.

STEP2:- Find the Maxterm & Minterm in the given expression.

STEP3:- Fill cell of K-map for SOP with 1 for Minterm.

STEP4:- Fill cell of K-map for POS with 0 for Maxterm.

STEP5:- We create rectangular groups that contains total

terms in the power of 2 like 1,2,4,8,16…….

STEP6:- With the help of these groups find POS  SOP simplifying expression.

2-Variable K-Map:-

The 2 variable K-Map is represented as an array of four cell.

Number of cells :-  2n = 22 = 4 cells

Three Variable k-map:-

The 3 variable k-map is represented as an array of 8 cells.

Number of cells :-  2n = 23 = 8 cells.

Q:- F= Ʃm(0,2,3,4)

                        

Y = B’C’ + A’B

Q:- F=Ʃm(0,1,2,5)

Y = B'C + A'C'

4-Variable K-Map:-

The 4 variable k-map is represented as an array of 16 cells.

Number of cells :-  2n = 24 = 16 cells

Combinational logic circuit

Combinational logic circuits are the circuits that contains different type of logic gates.

At any instant of time, the output of combinational circuits depends only on the present input terminals.

     

 The combinational logic circuits does not have any backup or previous memory. The present state of the circuits is not affected by the previous state of the input.

The n number of input and m number of output are possible in combinational logic circuits.

Design of combinational circuits:-

Design of combinational circuits starts from the verbal outline of the problem & end in a logic circuit diagram.

The procedure involves following steps:- 

1. States the given problem completely & exactly.

2. Interpret the problem to determine available input variables & required output variables.

3. Assign a letter symbol to each input variable and each output variable.

4. Design a truth table that defines the required relations b/w inputs and outputs.

5. Obtain simplified boolean expression for each output.

6. Draw a logic circuit diagram to implement the boolean expressions.

Examples of Logic Combinational Circuits:-

Q:- Design a Combinational Circuits with Two inputs, Which produce as logic 0 when any of the input is 1?

1. Truth Table

2. Boolean Expression

3. Logic Diagram

A	B	Y
0	0	1
0	1	0
1	0	0
1	1	0

Q:- Consider a Combinational Circuit whose output is 0 if the input variable have more 1’s than 0, The output is 1 otherwise. Design 3-bit circuit with this  Logic by generating the.

1. Truth Table

2. Boolean Expression 

3. Logic Diagram

A	B	C	F
0	0	0	1
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	0

    

What is Adders?

The address is a combinational circuits that performs addition of bits/binary number is called adders.

Types of Adders

There are two types of adders

1. Half Adder  2. Full Adder

Half Adder:- A Combinational Circuits that performs the addition of two binary digits is called Half Adder. It receives two inputs and produces two outputs sum & carry.

C = A.B                                        S = A’B+AB’

2. Full Adder:- A Combinational Circuits that performs the addition of three binary digits is called full adder. It receives three inputs & produces two output sum & carry.

S = A’B’C+A’BC’+AB’C’+ABC,                C= AB+BC+AC

Q. Design & implementation 2 half adder using Full Adder?

ENCODER

It is multiple input & multiple output device. Encoder is combinational circuits that converts 2n lines of input into n lines of output. It is the reverse process of decoder. Only one input is activated at a time. Encoders are used to convert data from one for to another form. It converts analog signal to digital signal. It mainly used in telecommunication, networking etc. to transfer data from one end to another end. For easy transmission in digital system encoder encrypts data in codes and then transmitted.

Design & implementation using 4 to 2 encoder?

Design & implementation using 8 to 3 encoder?

DECODER

It is multiple input & multiple output device. Decoder is a Combinational

Circuits that converts n lines of input into 2nlines of output. Applications of decoders are converting binary code

to other code like;

Binary to Octal 3x8

Binary to Hexadecimal 4x16

Binary to Decimal 4x10

2 to 4 decoder

Design & implementation a Full Adder Circuit using 3:8 Decoder?

Y	A	B	C	S(SUM)	C (CARRY)
y0	0	0	0	0	0
y1	0	0	1	1	0
y2	0	1	0	1	0
y3	0	1	1	0	1
y4	1	0	0	1	0
y5	1	0	1	0	1
y6	1	1	0	0	1
y7	1	1	1	1	1

SUM = Y1+Y2+Y4+Y7

CARRY = Y3+Y5+Y6+Y7

Design 4x16 decoder using 3x8 decoder?

A3	A2	A1	A0	O/P
0	0	0	0	Y0
0	0	0	1	Y1
0	0	1	0	Y2
0	0	1	1	Y3
0	1	0	0	Y4
0	1	0	1	Y5
0	1	1	0	Y6
0	1	1	1	Y7
1	0	0	0	Y8
1	0	0	1	Y9
1	0	1	0	Y10
1	0	1	1	Y11
1	1	0	0	Y12
1	1	0	1	Y13
1	1	1	0	Y14
1	1	1	1	Y15

MULTIPLEXER:-

Multiplexer is a combinational circuits that has 2n inputs, n selection lines & single output lines. Multiplexer is also known as data selector. Binary information is received from the input lines & directed to the output lines on the basic of the value of selection lines.

Truth Table :- 

S	Y
0	I0
1	I1

Y = S’A + SB

Circuits Diagram

Application :- 

1. Communication system

2. Computer Memory

3. Networking

4. Transmission from the computer to a satellite.

Advantages:-

1. Reduces number of wires

2. Reduces circuit complexity & cost

3. Widely used in todays communication & networking

Design & implementation using 4:1 mux?

Programmable Logic Array (PLA):- 

A programmable logic array (PLA) is a kind of programmable logic device used to implement combinational logic circuits. The PLA has a set of programmable AND gate planes. Which links to a set of programmable OR gate planes. Which can then be conditionally complemented to produce an output. It has 2n AND gate for N input variable & for M OR gats, each with programmable inputs from all of the AND gates. This layout allows for many logic function to be synthesized in the sum of product canonical form.

Implementation Procedure -

1. Preparation in SOP (Sum of Product) from.

2. Obtain the minimum SOP from to reduce the number of product terms to a minimum.

3. Decide the input combination of the AND matrix for generating the required product term.

4. Then decide the input connections of the OR matrix to generate the sum terms.

5. Decide the connections of the inversion matrix.

6. Program the PLA

1st Block	2nd Block	3rd Block	4th Block	5th Block
Input Buffer	AND Matrix	OR Matrix	Invert/Non-InvertMatrix	Flip-Flop o/p Buffer

Implement the following function using PLA.

F(a,b,c) = Ʃm (0,3,4,7)

F(a,b,c) = Ʃm (1,2,5,7)

Ans:-  F(a,b,c) = Ʃm (0,3,4,7)

F(a,b,c) = Ʃm (1,2,5,7)

READ ONLY MEMORY (ROM):

ROM is a memory device in which a fixed set of binary information is stored.

It includes decoder & OR gates. ROM come with internal links that can be fused or broken.

M = number of bits in word.

A	B	F1	F2
0	0	0	1
0	1	1	0
1	0	1	1
1	1	1	0

Q:- What is sequential circuits?

Ans:- Sequential Circuit is a special type of circuit that has a series of input & output.

The output of sequential circuits depends on both the combination of present input & previous output (Present State).

Differential b/w combinational circuit & sequential circuit?

There are Two types of Sequential Circuits.

Sl No.	Synchronous Sequential Circuits	Asynchronous Sequential Circuits
1.	Sequential Circuits which are controlled by clock are called Synchronous Sequential Circuits	The Sequential Circuits Which are not controlled by a clock are Asynchronous Sequential Circuits
2.	The change in input signal affect memory elements only on activation of clock signal.	The change in input signals can affect memory elements at any instant of time.
3.	Slower than asynchronous because depends on clock.	Faster than synchronous sequential circuit due to absent.

FLIP-FLOP:- 

Q:- What is flip-flop? Full Explanation?

Ans:- Flip-Flop is sequential circuit that is used to store/hold 1 bit binary data as well as construct a register as called flip-flop.

• Flip-Flop has two state set & clear.

  

1. Set = current (1)

2. Clear = No Current (0)

 Note:-  We can create/made up flip-flop by two ways.

1. Using NOR Gate

2. Using NAND Gate

Types of Flip-Flop:-

There are many types of flip-flop.

1. R-S Flip-Flop (NOR) / S-R Flip-Flop (NAND)

2. J-K Flip-Flop

3. D Flip-Flop

4. T fLIP-Flop

5. Master-Slave Flip-Flop

Block Diagram

Flip-Flop Latch:-

What is Latch? Full Explanation?

Ans:- Latch are the basic building block of the sequential circuit that is used to construct/make flip-flop is called Latch.

It store/hold data 1 bit binary data at a time and change its output immediately based on the new input data.

We use logic gate to make latch -

Types of Latch-

a.) R-S Latch (UsingNOR Gate) / S-R Latch (Using NAND Gate)

b.) J-K Latch

c.) D Latch

d.) T Latch

a.) R-S Latch (Using NOR Gate)

Step - I (Logic Circuit)

NOR Gate truth table
A	B	Y = (A+B)’
0	0	1
0	1	0
1	0	0
1	1	0

If any input are 1 then output will be 0(zero).

Step -II (Truth Table)

R	S	Q	Q’	Remark
0	0	1	0	No change / Previous state
0	1	1	0	Set state
1	0	0	1	Clear / Reset state
1	1	0	0	Invalid / Not allowed state

Block Diagram

S-R Latch using NAND Gate-

Step - I Circuit Diagram

NAND Gate truth table
A	B	Y = (A.B)’
0	0	1
0	1	1
1	0	1
1	1	0

If any input are 1 then output will be 0(zero).

Step - II Truth Table-

S	R	Q	Q’	Remark
0	0	1	1	No change / Previous state
0	1	1	0	Set state
1	0	0	1	Clear / Reset state
1	1	0	1	Invalid / Not allowed state

Step - III Block Diagram

R-S FLIP-FLOP with clock using NOR Gate

Step - I (Circuit Diagram)

AND Gate Truth Table
A	B	Y = A.B
0	0	0
0	1	0
1	0	0
1	1	1

Step -II (Truth Table)

CLK	R	S	Q	Q’	Remark
1	0	0	1	0	No change / Previous state
1	0	1	1	0	Set State
1	1	0	0	1	Clear / Reset State
1	1	1	0	0	Invalid / Not Allowed

Step - III (Block Diagram)

S-R FLIP-FLOP WITH CLOCK USING NAND GATE

Step - I, Circuit Diagram

NAND Gate Truth Table
A	B	Y = A.B
0	0	1
0	1	1
1	0	1
1	1	0

If all input zero(0), then output will be 1.

Step - II, Truth Table

CLK	S	R	Q	Q’	Remark
1	0	0	0	1	No change / Previous state
1	0	1	0	1	Clear / Reset State
1	1	0	1	0	Set State
1	1	1	1	1	Invalid / Not Allowed

Step - III, Block Diagram

J-K Latch using NOR Gate

Step - I, Circuit Diagram

J-K LATCH

Step - II, Truth Table

J	K	Q	Q’	Remark
0	0	1	0	No change / Previous state
0	1	1	0	Set state
1	0	0	1	Clear / Reset state
1	1	1	0	Toggle Condition

Step - III, Block Diagram

J K Latch using NAND Gates:-

Truth Table:- 

J	K	Q	Q’	Remark
0	0	0	1	No change / Previous state
0	1	0	1	Clear / Reset state
1	0	1	0	Set state
1	1	0	1	Toggle Condition

J-K Flip-Flop with clock using NOR Gate:- 

Step - 1 :- Circuit Diagram

A	B	A+B
0	0	0
0	1	0
1	0	0
1	1	1

Step - 2:- Truth Table

Clock	J	K	Q	Q’	Remark
1	0	0	1	0	No Change
1	0	1	1	0	Set State
1	1	0	0	1	Clear/Reset State
1	1	1	1	0	Toggle Condition

Step - 3 :- Block Diagram

J-K Flip-Flop with clock using NAND Gate:-

Step  - 1:- Circuit Diagram

A	B	(A+B)’
0	0	1
0	1	1
1	0	1
1	1	0

Step - 2:- Truth Table

Clock	J	K	Q	Q’	Remark
1	0	0	0	1	No Change
1	0	1	0	1	Clear/Reset State
1	1	0	1	0	Set State
1	1	1	1	0	Toggle Condition

Step - 3:- Block Diagram

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