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PDF Drive is your search engine for PDF files. As of today Switching Theory And Logic Design UNIT-I Number System and Boolean Algebra and Switching. This textbook explains the "why, what and how" behind all concepts and emphasizes on the application, implementation, design, development. (R15A) SWITCHING THEORY AND LOGIC DESIGN. OBJECTIVES. This course provides in-depth knowledge of switching theory and the logic design.

Faye Yturralde. D input, no matter how that changes. Sequential Networks Pages Rojas Jr. Classification of Switching Functions Pages Free Preview. Flag for inappropriate content.

Table of Contents: Electrical Power System. Objective Electrical Technology. Power Plant Instrumentation. Signals And Systems. Modern Control Engineering. Digital Communications.

Control System Design. Anand Kumar. Classification of Switching Functions Pages Synthesis with Multiplexers Pages Realizations with ROM Pages Realizations with Programmable Logic Arrays Pages Universal Cellular Arrays Pages Field Programmable Logic Arrays Pages Sequential Networks Pages Realization of Sequential Networks Pages Show next xx.

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Recommended for you. The digit in A is calculated and written on a new line, shifted second column from the right is added: The in B that was used. The sum of all these partial products third column: This time, a 1 is carried, B B.

Since there are only two digits in binary, there are only goes into the first three digits of the dividend B B B B. In decimal, 27 divided by 5 is 5, with Here, the divisor is , or 5 decimal, while the B B. The procedure is the B B. Our last group of Boolean identities is perhaps the less power, and run faster than complex circuits. Boolean functions to their simplest form. We give our identities using both forms. Our first group is rather intuitive:. We can use Boolean identities to simplify the function: Our second group of Boolean identities should be familiar to you from your study of algebra:.

This simplifications.

Each line gives a form of the expression, step uses the fact that or and the rule or rules used to derive it from the previous distributes over and.

It one. Generally, there are several ways to reach the result. T Identity Law. Subtraction Identity. Solve the Boolean expression by using different laws: The AND gate is so named because, if 0 is called "false" Keep in mind that computers work on an electrical flow and 1 is called "true," the gate acts in the same way as where a high voltage is considered a 1 and a low voltage the logical "and" operator.

The following illustration and is considered a 0. Using these highs and lows, data are table show the circuit symbol and logic combinations for represented. Electronic circuits must be designed to an AND gate.

In the symbol, the input terminals are at manipulate these positive and negative pulses into left and the output terminal is at right.

The output is meaningful logic. Combinations of logic gates form circuits designed with specific tasks in mind. For example, logic gates are combined to form circuits to add binary numbers adders , set and reset bits of memory flip flops , multiplex multiple inputs, etc.

Input 1 Input 2 Output. A logic gate is an elementary building block of a digital 0 0 0 circuit.

Most logic gates have two inputs and one output. The logic state of a terminal can, 1 1 1 and generally does, change often, as the circuit processes data. In most logic gates, the low state is approximately zero volts 0 V , while the high state is approximately 3.

The OR gate gets its name from the fact that it behaves after the fashion of the logical inclusive "or. It acts in the manner of the logical operation Input 1 Input 2 Output "and" followed by negation.

The output is "false" if both 0 0 0 inputs are "true. It reverses the logic state. Its output is "true" if both inputs are "false.

Input 1 Input 2 Output 3. Its output is "true" if the inputs are the same and "false" if the inputs are different. Using combinations of logic gates, complex operations can be performed. In theory, there is no limit to the number of gates that can be arrayed together in a single device.

But in practice, there is a limit to the number of Input 1 Input 2 Output gates that can be packed into a given physical space. Arrays of logic gates are found in digital integrated 0 0 0 circuits ICs. As IC technology advances, the required 0 1 1 physical volume for each individual logic gate decreases and digital devices of the same or smaller size become 1 0 1 capable of performing ever-more-complicated operations 1 1 0 at ever-increasing speeds.

They can also be combined to substitute one type of gate for another. For example the truth table on Inputs Outputs reduce the number of gate inputs or substitute one type of the right show the intermediate gate for another. The diagram shows this for a 2-input NAND gate. This can be Note that AND and OR gates cannot be used to create wasteful if only a few gates are required unless they are other gates because they lack the inverting NOT all the same type.

To avoid using too many ICs you can function. Then simplify the system by deleting adjacent pairs of NOT gates marked X above. This can be done because the second NOT gate cancels the action of the first.

The final system is shown below. This is better than the original system which required three ICs one for each type of gate. Substituting NAND or NOR gates does not always increase the number of gates, but when it does as in this example the increase is usually only one or two gates. The real benefit is reducing the number of ICs required by using just one type of gate.

For this concern, primarily we should know the symbolic representation of each operation i. OR, AND etc. Following are the different symbols to represent different gates or Considering the above circuitry, break it into the gate operations: See below for the specific expression of all gates: Here we achieve the final and complex expression of the given logic circuit in Eq.

As we can remind that inverting the original signal two times will give you the original signal again which reflects that two times inversion will not effect the Boolean expression, so it can be eliminated. Output pattern of any circuit is the major concern for any designer. Again the same simple circuit It might be a traditional 0 or 1.

For example we have the following condition to one …Cheers. Number of possible combination for the construct a circuit for a specified output: Now the total logical gates we have to satisfy the condition of input. It possible combinations for the input are 8 23 and they P P is known that the functionality of AND gate is that it are stated below with their respective output: Then we should have any gate which checks 5 1 0 0 0 the output of AND and input C.

Now the final As stated earlier that the major concern to design any circuit we achieve is: Here we will discuss how to create a circuit when the conditions of inputs are given to get any particular output. Find the circuit on behalf of the following Boolean expressions: Find the Truth Tables of the circuits constructed 1 0 0 0 0 in the above part 1.

Construct circuits which fulfills the following 3 0 1 0 0 condition with required output pattern: Output should be high on these You can verify the above truth table by applying all the conditions. I suppose that you will b. Circuit 2 the same output. The full-adder circuit adds three one-bit binary numbers 6. The full-adder is usually a The half adder is an example of a simple, functional component in a cascade of adders, which add 8, 16, 32, digital circuit built from two logic gates.

The half adder etc. The carry input for the full-adder adds to one-bit binary numbers AB. The output is the circuit is from the carry output from the circuit "above" sum of the two bits S and the carry C.

The carry output from the full adder is fed to another full adder "below" itself in the cascade. Note how the same two inputs are directed to two different gates. The y column in the truth table shows all the 0 and 1 values associated with the gate's output. Similarly, all of the output values could be entered into the Karnaugh 7. However, for reasons of clarity, it is common for only a single set of values to be used, typically the 1s. Karnaugh maps provide an alternative technique for Similar maps can be constructed for 3-input and 4-input representing Boolean functions.

For example, consider functions. In the case of a 4-input map, the values the Karnaugh map for a 2-input AND gate. Unlike a truth table, in which the input values typically follow a standard binary sequence 00, 01, 10, 11 , the Karnaugh map's input values must be ordered such that the values for adjacent Karnaugh maps for 3-input and 4-input functions. This ordering is known as a gray code, and it is a key factor in the way in which Karnaugh maps work.

Such pairs of minterms and minimization of Boolean functions. Consider an can be grouped together and the variable that differs can example 3-input function represented as a black box with be discarded Figure 4. Note that the values assigned to the y output in the truth table were selected randomly, and have no significance beyond the purposes of this example.

Karnaugh map minimization of example 3-input function. In the case of the horizontal group, input a is 0 for both Example 3-input function. Thus, for this group, changing The equation extracted from the truth table in sum-of- the value on b does not affect the value of the output. Algebraic simplification the equation representing this group.

Similarly, in the techniques could be employed to minimize this equation, case of the vertical group, input a is 1 for both boxes, but this would necessitate every minterm being input b is 0 for both boxes, and input c is 0 for one box compared to each of the others which can be somewhat and 1 for the other.