WORKING PRINCIPLE OF DIGITAL LOGIC CHAPTER - 4 WORKING PRINCIPLE OF DIGITAL LOGIC A logic gate is an elementary building block of a digital circuit. It is a circuit with one output and one or more inputs. At any given moment, logic gate takes one of the two binary conditions low (0) or high (1), represented by different voltage levels. A voltage level will represent each of the two logic values. For example +5V might represent a logic 1 and 0V might represent a logic 0

FUNDAMENTAL LOGIC GATES CHAPTER - 4 FUNDAMENTAL LOGIC GATES AND OR NOT UNIVERSAL LOGIC GATES NAND NOR OTHER GATES XOR XNOR

LOGIC GATES

BUBBLED AND GATE

Bubbled AND Gate truth table A B C 0 0 1 0 1 0 1 0 0 1 1 0 You can see that, a bubbled AND gate produces the same output as a NOR gate. So, you can replace each NOR gate by a bubbled AND gate. In other words the circuits are interchangeable. Therefore ( A + B ) = A . B which establishes the De Morgan’s first theorem.

Bubbled OR gate

Conversion of Boolean Expression Truth table lists all the values of the boolean function for each set of values of the variables. Now we will obtain a truth table for the following boolean function D = (A · B) + C Clearly, D is a function of three input variables A, B, and C. Hence the truth table will have 2 to the power 3 = 8 entries, from 000 to 111. Before determining the output D in the table, we will compute the various intermediate terms like A · B and C as shown in the table below. For instance, if A = 0, B = 0 and C = 0 then D = ( A . B ) + C = ( 0 . 0 ) + 0 = 0 + 0 = 0 + 1 = 1 Here we use the hierarchy of operations of the boolean operators NOT, AND and OR over the parenthesis. The truth table for the boolean function is

Converting a Boolean Equation to a Logic Circuit The boolean function is realized as a logic circuit by suitably arranging the logic gates to give the desired output for a given set of input. Any boolean function may be realized using the three logical operations NOT, AND and OR. Using gates we can realize boolean function. Now we will draw the logic circuit for the boolean function. E = A + ( B · C ) + D This boolean function has four inputs A, B, C, D and an output E. The output E is obtained by ORing the individual terms given in the right side of the boolean function. That is, by ORing the terms A, ( B · C ) and D.

Converting a Logic Circuit to a Boolean Function As a reversal operation, the realization of the logic circuit can be expressed as a boolean function. Let us formulate an expression for the output in terms of the inputs for the given the logic circuit

Result

ADDERS The circuit that performs addition within the Arithmetic and Logic Unit of the CPU are called adders.

HALF ADDER & FULL ADDER A unit that adds two binary digits is called a half adder and the one that adds together three binary digits is called a full adder.

The Flip-Flop A flip flop is a circuit which is capable of remembering the value which is given as input. Hence it can be used as a basic memory element in a memory device. These circuits are capable of storing one bit of information. Basic flip-flops A flip-flop circuit can be constructed using either two NOR gates or two NAND gates. By cross-coupling two NOR or NAND gates, the basic operation of a flip-flop could be demonstrated. In this circuit the outputs are fed back again to inputs.

CROSS COUPLING

PRACTICAL CONTINUES END