UNIT 1 COMPUTER SYSTEM DIGITAL LOGIC AND LOGIC GATES

 Q: define digital and logic gates

1. Digital: "Digital" refers to the representation of information or data using discrete symbols or values, typically expressed in binary digits (bits), which can take on one of two possible states: 0 or 1. In the context of electronics and computing, digital systems manipulate these binary digits to perform various operations, such as arithmetic, logic, and data processing.

2. Logic Gates: Logic gates are fundamental building blocks of digital circuits. They are electronic devices or circuits that perform Boolean logic operations on one or more input signals to produce an output signal based on predetermined logical rules. There are several types of logic gates, each corresponding to a specific logical operation:

• AND Gate: Produces a HIGH output (1) only if all of its inputs are HIGH.
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• OR Gate: Produces a HIGH output (1) if any of its inputs are HIGH.
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• NOT Gate: Also known as an inverter, it produces the logical complement of its input.
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• NAND Gate: Produces a LOW output (0) only if all of its inputs are HIGH.
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• NOR Gate: Produces a LOW output (0) if any of its inputs are HIGH.
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• XOR Gate: Produces a HIGH output (1) if the number of HIGH inputs is odd.
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• XNOR Gate: Produces a HIGH output (1) if the number of HIGH inputs is even.
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   Q: What is Truth table ?

10. A truth table is a tabular representation that shows all possible combinations of input values for a logical expression or a logic gate, along with the corresponding output values. It provides a systematic way to determine the output of a logical expression or gate for every possible input combination.

11. Let's illustrate a truth table for a simple logic gate, the AND gate:

    

    In this truth table:

    • Inputs A and B represent the two input signals to the AND gate.
    • Output represents the resulting output signal produced by the AND gate for each combination of input values.
    • Each row of the truth table represents a unique combination of input values.
    • The output value (0 or 1) is determined by the logical operation performed by the AND gate. In this case, the output is 1 (HIGH) only when both inputs are 1; otherwise, it is 0 (LOW).

    You can create similar truth tables for other logic gates, such as OR, NOT, NAND, NOR, XOR, etc., by considering all possible combinations of input values and determining the corresponding output values based on the logical operation performed by each gate.

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    Q: Explain boolean identities with example

13. Boolean identities are fundamental rules governing the behavior of boolean expressions. They define how boolean variables and logical operators interact with each other. Understanding these identities is essential for simplifying, analyzing, and manipulating boolean expressions effectively. Here are some key boolean identities:

    1. Identity Laws:

       • Identity for AND: In an AND operation, if one operand is true and the other operand is true, the result is true. Similarly, if one operand is false, regardless of the other operand's value, the result is false.
         • $�\wedge 1=�$: ANDing a variable with true (1) results in the variable itself.
         • $�\wedge 0=0$: ANDing a variable with false (0) results in false.
       • Identity for OR: In an OR operation, if one operand is true, regardless of the other operand's value, the result is true. Similarly, if one operand is false and the other operand is false, the result is false.
         • $�\vee 0=�$: ORing a variable with false results in the variable itself.
         • $�\vee 1=1$: ORing a variable with true results in true.

    2. Domination Laws:

       • Domination for AND: If one operand in an AND operation is false, regardless of the other operand's value, the result is false.
         • $�\wedge 0=0$
       • Domination for OR: If one operand in an OR operation is true, regardless of the other operand's value, the result is true.
         • $�\vee 1=1$

    3. Complement Laws:

       • Complement for AND: The AND operation between a variable and its complement (negation) results in false.
         • $�\wedge \mathrm{\neg }�=0$
       • Complement for OR: The OR operation between a variable and its complement (negation) results in true.
         • $�\vee \mathrm{\neg }�=1$

    These identities provide the basis for simplifying boolean expressions using algebraic techniques, such as substitution, factoring, and distribution. By applying these rules, complex expressions can often be reduced to simpler forms, facilitating analysis and implementation in digital logic circuits and programming.

1. Multiple Choice Questions
15. Certainly! Here are some multiple-choice questions (MCQs) related to digital and logic gates: 1. Which of the following logic gates outputs a true (HIGH) signal only if all of its inputs are true? a) AND gate b) OR gate c) NOT gate d) XOR gate 2. How many input combinations are possible for a 2-input logic gate? a) 2 b) 3 c) 4 d) 8 3. Which logic gate is represented by the symbol "⊕"? a) OR gate b) AND gate c) XOR gate d) NAND gate 4. What is the output of an AND gate if one of its inputs is false? a) True (HIGH) b) False (LOW) c) Undefined d) Depends on the other input 5. Which logic gate produces a true (HIGH) output only if exactly one of its inputs is true? a) AND gate b) OR gate c) XOR gate d) NOT gate 6. In a NAND gate, what is the output when both inputs are true? a) True (HIGH) b) False (LOW) c) Undefined d) Depends on the specific NAND gate 7. Which logic gate is equivalent to a series combination of an OR gate and a NOT gate? a) AND gate b) NOR gate c) XOR gate d) NAND gate 8. How many input combinations are possible for a 3-input logic gate? a) 2 b) 3 c) 4 d) 8 9. Which logic gate has an output that is the inverse of its input? a) OR gate b) AND gate c) NOT gate d) XOR gate 10. What is the output of a NOR gate if both of its inputs are false? a) True (HIGH) b) False (LOW) c) Undefined d) Depends on the specific NOR gate Answers: 1. a) AND gate 2. c) 4 3. c) XOR gate 4. b) False (LOW) 5. c) XOR gate 6. b) False (LOW) 7. b) NOR gate 8. d) 8 9. c) NOT gate 10. a) True (HIGH)