Digital Logic Gates and Number Systems

Digital Logic Gates

• AND Gate: Output is 1 only if all inputs are 1
• OR Gate: Output is 1 if any input is 1
• NOT Gate: Output is the opposite of the input

Truth Tables

• AND Gate:
  • X | Y | Z
  • 0 | 0 | 0
  • 0 | 1 | 0
  • 1 | 0 | 0
  • 1 | 1 | 1
• OR Gate:
  • X | Y | Z
  • 0 | 0 | 0
  • 0 | 1 | 1
  • 1 | 0 | 1
  • 1 | 1 | 1
• NOT Gate:
  • X | Y
  • 0 | 1
  • 1 | 0

Logic Gates - OR, AND, NOT

• XOR Gate: Output is 1 if only one input is 1.
• XNOR Gate: Output is 1 if both inputs are the same (either both 0 or both 1).
• NAND Gate: Output is 0 if all inputs are 1, otherwise 1.
• NOR Gate: Output is 1 only if all inputs are 0

Universal Gates

• NAND gate: Can implement any logic function
• NOR gate: Can implement any logic function

Number Systems

• Decimal: Base-10 system
• Binary: Base-2 system (0s and 1s)
• Octal: Base-8 system (0-7)
• Hexadecimal: Base-16 system (0-9, A-F)

Codes

• BCD (Binary Coded Decimal): Represents each decimal digit with a 4-bit binary code.
• Excess-3 code: A BCD code where each decimal digit is represented by a 4-bit code that is 3 greater than the decimal equivalent
• Gray Code: Each successive code differs by only one bit

Binary Arithmetic

• Addition: Perform binary addition using rules for carry propagation.
• Subtraction: Use 1's complement or 2's complement to perform subtraction in binary.

Boolean Algebra

• De Morgan's Theorem: (A + B)' = A' . B' and (A . B)' = A' + B'
• Absorption theorem: A + AB = A (and) A (A+B) = A
• Commutative property: A + B = B + A, A . B = B. A
• Associative property: (A + B) + C = A + (B +C) and ( A . B) . C = A . (B .C)
• Distributive property: A . (B + C) = AB + AC and A + B . C = (A + B) (A + C)

Error Detecting and Correcting Codes

• Parity bit: Extra bit added to a message to detect errors.
• Hamming code: A linear error-correcting code used for detecting and correcting single-bit errors.

Combinational Circuits

• Definition: O/Ps depends only on present i/ps
• Examples: adders, subtractors, encoders, decoders, multiplexers, demultiplexers, comparators

Sequential Circuits

• Definition: O/Ps depends on present i/ps and past i/ps
• Examples: Latches, flip-flops, counters

Registers

• Definition: Stores binary information
• Types: Serial IN/Serial OUT (SISO), Serial IN/Parallel OUT (SIPO), Parallel IN/Serial OUT (PISO), Parallel IN/ Parallel OUT (PIPO)

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This quiz covers the fundamental concepts of digital logic gates, including AND, OR, NOT, XOR, and NAND operations. It also explores different number systems such as decimal, binary, octal, and hexadecimal. Test your understanding of logic functions and truth tables!