logic circuits_walla2_c++_download_Welcome.pdf
- 2. 2 CMSC 250 Introduction Logic gates are the basic components in digital electronics. These gates are used to create digital circuits right from simple to complex logic circuit and even complex integrated circuits. Complex microprocessor or microcontroller ICs are constructed using many logic gates. Logic gates are the fundamental building blocks of all digital systems including computers. It has one or more inputs and one output with some logical relationship between them. Logic gate accepts binary signals i.e. True or False, ON or OFF, 1 or 0 and have an ability to make decisions
- 3. 3 CMSC 250 Introduction The state of the output is decided by the input states. All logic gates implements some Boolean function which correlates output with input through some logical operation. Logic gates are mainly designed with the electronic switches using diodes and transistors.
- 4. 4 CMSC 250 NOT gate NOT gate has one-input and one-output. It is a logic circuit whose output is always the complement of the input. The NOT gate is popularly known as inverter. It performs logical inversion or complementation. The logic symbol and the Truth table: R=~P
- 5. 5 CMSC 250 AND gate AND gate is a logic circuit having two or more inputs and one output. The AND gate performs logical multiplication. The output of an AND gate is HIGH only when all of its inputs are in the HIGH state. In all other cases, the output is LOW. For AND gate, Y = A.B The logic symbol and the truth table:
- 6. 6 CMSC 250 OR Gate An OR gate is a logic circuit with two or more inputs and one output. The OR gate performs logical addition. The output of an OR gate is HIGH only when all of its inputs are in the HIGH state. In all other cases, the output is LOW. For OR gate, Y = A + B. Logic symbol and truth table:
- 7. 7 CMSC 250 NAND gate NAND gate is combination of AND and NOT gates. The NAND gate provides AND functions with inverted output. The output of a NAND gate is a logic ‘0’ when all its inputs are a logic ‘1’. For all other input combinations, the output is a logic ‘1’. NAND gate operation is logically expressed as P | Q ≡ ∼(P ∧ Q) Symbol logic and truth table:
- 8. 8 CMSC 250 NOR gate NOR gate is combination of OR and NOT gates. The NOR gate provides OR function with inverted output. The output of a NOR gate is a logic ‘1’ when all its inputs are logic ‘0’. For all other input combinations, the output is a logic ‘0’. NOR gate operation is logically expressed as P ↓ Q ≡ ∼(P ∨ Q). the logic symbol and truth table:
- 9. 9 CMSC 250 XOR (Exclusive OR) gate An XOR gate is a two inputs and one output logic circuit. The output of an XOR gate is at logic ‘1’ when the inputs are dissimilar and at logic ‘0’ when the inputs are similar. The logic equation for two input XOR gate is given by X = A⊕B=A'B + AB’
- 10. 10 CMSC 250 XNOR gate XNOR is obtained by the combination of NOT and XOR gates. XNOR gate has a two inputs and one output. The output of an XNOR gate is at logic ‘1’ when the inputs are similar and at logic ‘0’ when the inputs are dissimilar. The following is the Boolean expression of the XNOR gate: Y = A ⊙ B= AB + A'B'
- 11. 11 CMSC 250 Universal Logic Gates Any Boolean / logic expression can be realized using the AND, OR, and NOT gates. From these three primary gates, two derived gates NAND and NOR are usually realized. It is possible to construct basic gates namely NOT, AND, OR using combination of NAND gates or a combination of NOR gates. For this reason NAND and NOR gates are called as universal logic gates.
- 12. 12 CMSC 250 NAND gate as universal logic gate
- 13. 13 CMSC 250 NAND gate as universal logic gate Xor gate:
- 14. 14 CMSC 250 NOR Gate as universal logic gate
- 15. 15 CMSC 250 NOR Gate as universal logic gate XOR gate:
- 16. 16 CMSC 250 Determining Output for a Given Input Indicate the output of the circuits shown below for the given input signals.
- 18. 18 CMSC 250 Constructing the Input/Output Table for a Circuit Construct the input/output table for the following circuit. Solution:
- 19. 19 CMSC 250 Finding a Boolean Expression for a Circuit Find the Boolean expressions that correspond to the circuits shown below.
- 21. 21 CMSC 250 Constructing Circuits for Boolean Expressions Construct circuits for the following Boolean expressions. a. (∼P ∧ Q) ∨ ∼Q b. ((P ∧ Q) ∧ (R ∧ S)) ∧ T
- 22. 22 CMSC 250 Designing a Circuit for a Given Input/Output Table Design a circuit for the following input/output table: (P ∧ Q ∧ R) ∨ (P∧ ∼Q ∧ R) ∨ (P∧ ∼Q∧ ∼R).
- 23. 23 CMSC 250 Simplifying Combinational Circuits Have the same truth table
- 24. 24 CMSC 250 Combining & determining I/O relationship From a circuit to a Boolean formula: p ~(q ^ r) p q r
- 25. 25 CMSC 250 Draw a circuit for: p, q & r are inputs. Simplify before building the circuit. p q r output 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0