Flip-Flops

Overview about Flip-Flops

FAQ’s

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     What is Flip-flops?

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      • How to use Flip flops?

•         • How to implement flip-flops using the sequential logic circuit?

•        • These are the “frequently asked questions” about flip-flops discussions.

•        • We will answer every question that is given about using flip-flops.

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Overview about flip-flops

What is Flip-flops?

•       is a BI stable device it can store single bit either 0 or 1.

•        has two output, they are complement to each other. 

•        Today, the term flip-flop has come to mostly denote non-transparent (clocked or edge-triggered) devices, while the simpler transparent ones are often referred to as latches;

•        however, as this distinction is quite new, the two words are sometimes used interchangeably.  

•        controlled by one or two control signals and/or a gate or clock signal.

•        The output often includes the complement as well as the normal output.

•        are implemented electronically, they require power and ground connections.

• How to use Flip-Flops?

               

     -  Flip flops is a clock signal. It is used to trigger (activate) the sequential logic circuits. Further it is classified as raising (positive) edge clock signal and falling (negative) edge clock signal.

           • These are the output of Q in waveform together with the clock and J K data inputs.

By looking at the table 1, we can say that in the first positive rising of the clock, the output of Q will be set to 1 in response to the J K data inputs which is J = 1 and K = 0 

Again, we have arrived to the next rising edge of the clock. By looking at the table 1, the output of the Q will be toggled.

 Next….

The output of Q becomes toggled again because data input of J and K are both 1

And so on.. 

THE KARNAUGH MAP

What is Karnaugh Map?

    Karnaugh Map - is a method to simplify Boolean algebra expressions. The Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability, also permitting the rapid identification and elimination of potential race conditions.

OVERVIEW OF KARNAUGH MAP

    In a Karnaugh map the boolean variables are transferred (generally from a truth table) and ordered according to the principles of Gray code in which only one variable changes in between adjacent squares. Once the table is generated and the output possibilities are transcribed, the data is arranged into the largest possible groups containing 2ⁿ cells (n=0,1,2,3...)^[1] and the minterm is generated through the axiom laws of boolean algebra.

 WHAT'S MORE ABOUT KARNAUGH MAP OR K-MAP?

    We will going to discussed about karnaugh maps (k-maps) and we have been discussing about truth tables where we have got our input and output variables. Since the truth table's binary and decimal numbers were being read respectively with the assigned input and output variables unlike the K-map. K-map's binary input and output variable together with the binary and decimal numbers were recognized in rows and in columns. The simple representation of truth table vs k-map are the following:

HOW TO IMPLEMENT K-MAPS?

   To implement k-maps, first we should consider it's minterms, what is minterms? minterm is a Boolean expression resulting in 1 for the output of a single cell, and 0s for all other cells in a Karnaugh map, or truth table. Supposedly, we have two statements or two inputs with one output. Since 2^n = 2^2 = 4, so we have four rows and the decimal numbers are counted up to 0, 1, 2, 3, and 4. Therefore, we have two rows and two columns for our k-map. Hence, putting the output 'F' in the k-map table, we can have our boolean expression 'A + B = F' to be able to get our logic or schematic diagram. Schematic diagram will be tackled on the proceeding blog.

BASIC LOGIC GATES

     AND gate – AND gate has two or more inputs and outputs. The AND gate produces a logic 1 at its output only when all of the inputs are high. A logic low state is produced when one or more of the inputs are low. The schematic diagram for AND gate is: 

 

     figure 1.

    

    OR gate – the or gate is a logic device that has two or more inputs and one output. The OR gate produces a logic 1 when one or more of its inputs are high. A logic 0 is produced only when all of the inputs are low.

   figure 2.

    NOT gate – the NOT gate or the inverter is a logic device that only has one input and one output. The inverter performs the logic function called the inversion or complementation, which means it changes the logic level applied to its input to the opposite logic level at its output. the schematic diagram of NOT gate:

               figure 3.

WHAT IS TRUTH TABLE?

     A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus.

OVERVIEW ABOUT THE TRUTH TABLE

     Alright, so now let’s do an example of a truth table that has 2 statements. So the first thing you need to know to plan is that since we have two statements will have 2^n and our  ‘n’ now is 2 based on the number of statements or inputs you have assigned. So we can obtain 4 rows about the given number of statements or inputs. Look to the figure 1 that I have set up:                 

A B 

0 0

0 1

1 0

1 0

figure 1:

     Practically, a truth table is composed of one column for each input variable (for example, A and B), and one final column for all of the possible results of the logical operation that the table is meant to represent. Each row of the truth table therefore contains one possible configuration of the input variables (for instance, A=true B=false), and the result of the operation for those values. So we can still say that the zero's '0' is false and ones's '1' is true in the truth table                                                                                                   

therefore, the new table is like:

A B 

F F

F T

T F

T T

    For example, if we have a simple boolean expression A + B = F. The output in the truth table becomes

A B   A + B   Z

F F        F      F

F T        T      T

T F        T      T

T T        T      T

Binary Arithmetic: Addition & Subtraction

 BINARY ARITHMETIC ADDITION AND SUBTRACTION

BINARY ADDITION

         
          There are some basic rules that we need to consider in the binary arithmetic addition. The examples for the binary arithmetic additions are the following:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10;

            Notice the 0 + 0, 0 + 1 & 1 + 0 have one place and 1 + 1 has two places. How would the digital systems handle this?. Well, it breaks it up this fashion. The sum of 1 + 1 is equal to 0 and it has a carry 1 (like the natural mathematic we had) just like a decimal systems on having a decimal addition including the “carry”. For example, 27 + 15 = 42  , we know that the sum of these two numbers is equal to “42”. The second number on the sum value which is the “2” is the sum of “7 plus 5” is equal to “12” and we know that the first number is the carry from the sum value, then the carry was added to the “2 plus 1” numbers which is equal to “4”. Since the “1 plus 2 plus the carry 1” is equal to “4” the same as the binary arithmetic addition by considering its binary values like for example:
                                                                    11
                                                                    101  =    5
                                                                 + 011  = + 3 
                                                                   1000  =   8
                                                                      figure 1.

the counting of binary numbers is from right to left 2^n..... 8, 4, 2, 1. In the figure 1, notice that the equivalent of the decimal number "5" is equivalent to a binary number "1 0 1"

BINARY SUBTRACTION

In Arithmetic subtraction, we need to have borrows unlike arithmetic addition. Arithmetic subtraction is just similar to natural mathematics subtraction and we can subtract one binary number from another by using the standard techniques adapted for decimal numbers. These are the examples of arithmetic subtraction:

 0 - 0 = 0

0 - 1 = 1 since 0 – 1 is equal to -1, we need to borrow another binary number 2 to left so that we can have a positive binary and decimal number

1 - 0 = 1

1 - 1 = 10

      Another example in the binary arithmetic subtraction are following:
      11 = 3 
     -10 = 2                                                                                
       01 = 1