XI STANDARD [ COMPUTER SCIENCE ] 5 MARKS STUDY MATERIAL.
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1 XI STANDARD [ COMPUTER SCIENCE ] 5 MARKS STUDY MATERIAL
2 HALF ADDER 1. The circuit that performs addition within the Arithmetic and Logic Unit of the CPU are called adders. 2. A unit that adds two binary digits is called a half adder 3. A half adder sums two binary digits to give a sum and a carry. TRUTH TABLE: FULL ADDER 1. The circuit that performs addition within the Arithmetic and Logic Unit of the CPU are called adders. 2. A unit that adds three binary digits is called a full adder 3. Here A, B referred as the inputs, C1 as carry input from the previous stage, C2 as carry output and S as sum. TRUTH TABLE: Input Sum Min Carry Min Input Output terms term A B C1 C2 S A B S of S C of C Ā.B A.B BOOLEAN FUNCTIONS: Sum: S = Carry: C = A. B LOGICAL CIRCUIT: BOOLEAN FUNCTIONS: Sum: Carry: LOGICAL CIRCUIT: In a half adder, an AND gate is added in parallel to the XOR gate to generate the carry and sum respectively. The full adder can be constructed from two half adders and an OR gate.
3 FLIP FLOP: 1. A flip flop is a circuit which is capable of remembering the value which is given as input. 2. The flip-flop circuit is an example of sequential circuit. 3. These circuits are capable of storing one bit of information. 4. A flip-flop circuit can be constructed using either two NOR gates or two NAND gates. Flip Flop Circuit using NOR Gates ELECTRONIC WORKBENCH: 1. Electronic workbench is a simulation tool for electronic circuits. 2. It allows designing and analysing circuits without using actual instruments. 3. The workbench s click-and-drag operation makes editing a circuit fast and easy. 4. It is a windows compatible tool and follows the normal conventions of windows. 5. The circuit diagrams and the output of the simulated circuits can be printed or exported MultiSim: 6. Example for electronic workbench is Multisim 7. It offers a single, easy-to-use graphical This can be tabulated as interface for the design needs. 8. It also provides the advanced functionality you need to design from specifications. Flip Flop Circuit using NAND Gates STEPS INVOLVED IN DESIGNING A LOGIC CIRCUIT. Step 1: Statement of the problem. Step 2: Identify inputs and outputs. Two inputs, say A and B, and one output, say C. A block diagram for this system is The corresponding truth table is given as Step 3: Formulate truth table. The truth table for this problem is given below. Notice that the output is 1 if only one of the inputs is 1. Otherwise the output is 0.
4 Input Output A B C DIFFERENT TYPES OF LOGIC GATES There are three fundamental logic gates namely, AND, OR and NOT. Also we have other logic gates like NAND, NOR, XOR and XNOR. AND Gate: The output of AND is true only when both inputs are true, otherwise, the output is false. Step 4: Convert the truth table to a Boolean function. Identify the minterms for the rows in the truth table which have an output 1 Input Output Minterms A B C Ā.B OR Gate: The output of OR is true if either or both of the inputs are true. If both inputs are false, then the output is false. By ORing the minterms, we obtain the boolean function corresponding to the truth table as D = Ā.B + Step 5: Realization of the Boolean function into a Logic Circuit Diagram. The logic circuit diagram corresponding to this Boolean function is given below. NOT Gate: The NOT gate, called a logical inverter, has only one input. It reverses the logical state.
5 NOR Gate: The NOR gate circuit is an OR gate followed by an inverter. XNOR Gate The XNOR (exclusive-nor) gate is a combination XOR gate followed by an inverter. Truth table: NAND Gate: The NAND gate operates as an AND gate followed by a NOT gate. XOR Gate The output is true if either, but not both, of the inputs are true. The output is false if both inputs are false or if both inputs are true. Truth table:
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