# Study of Logic Gates and realization of Boolean functions using Logic Gates

### Objective:

1. Verification and interpretation of truth tables for AND, OR, NOT, NAND, NOR Exclusive OR (EX-OR), Exclusive NOR (EX-NOR) Gates.
2. Implement Boolean function F=xy+x’y’+y’z.

Theory:

1. Logic gates are electronic circuits which perform logical functions on one or more inputs to produce one output. There are seven logic gates. When all the input combinations of a logic gate are written in a series and their corresponding outputs written along them, then this input/ output combination is called Truth Table. OR, AND and NOT are basic gates. NAND, NOR are known as universal gates. Various gates and their working is explained here.
• AND GATE: The AND gate performs a logical multiplication commonly known as AND function. The output is high when both the inputs are high. The output is low level when any one of the inputs is low.
• OR GATE: The OR gate performs a logical addition commonly known as OR function. The output is high when any one of the inputs is high. The output is low level when both the inputs are low.
• NOT GATE: The NOT gate is called an inverter. The output is high when the input is low. The output is low when the input is high
•  NAND GATE: The NAND gate is a contraction of AND-NOT. The output is high when both inputs are low and any one of the input is low .The output is low level when both inputs are high.
• NOR GATE: The NOR gate is a contraction of OR-NOT. The output is high when both inputs are low. The output is low when one or both inputs are high.
• X-OR GATE: The output is high when any one of the inputs is high. The output is low when both the inputs are low and both the inputs are high.

Useful IC Pin Detail:

Apparatus / Component required:

 Sl No Component Specification Quantity 1 AND GATE IC 7408 1 2 OR GATE IC 7432 1 3 NOT GATE IC 7404 1 4 NAND GATE IC 7400 1 5 NOR GATE IC 7402 1 6 X-NOR GATE IC 7486 1 7 IC TRAINER KIT —— 1 8 PATCH CORD ——- As per required

Procedure:

1. Connect the trainer kit to ac power supply.
2. Connect the inputs of any one logic gate to the logic sources and its output to the logic indicator.
3. Apply various input combinations and observe output for each one.
4. Verify the truth table for each input/ output combination.
5. Repeat the process for all other logic gates.
6. Switch off the ac power supply.

Observations:

 GATE SYMBOL FUNCTION OBSERVATION TRUTH TABLE AND OR NOT NAND NOR X-OR

Theory:

A binary variable can take the value of 0 or 1. A Boolean function is an expression formed with binary variables, the two binary operators OR and AND, and unary operator NOT, parentheses, and an equal sign. For a given value of the variables, the function can be either 0 or 1. Boolean function represented as an algebraic expression may be transformed from an algebraic expression into a logic diagram composed of AND, OR, and NOT gates. . Every Boolean function can be realized by a And-Or-Not gates i.e. using AOI logic

F=xy+x’y’+y’z

Procedure:

1. Connect the trainer kit to ac power supply.
2. Verify the gates and make connections as per circuit diagram-A.
3. Apply various input combinations and observe output for each one.
4. Verify the truth table for each input/ output combination.
5. Repeat the process for circuit diagram-B.
6. Switch off the ac power supply.

Observations:

 INPUT OUTPUT X Y Z F

Conclusion: Should follow result in conformation with theory.

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