ملف ماث

• What is a logic gate?


  An elementary building block of a digital circuit
• How many inputs and outputs do most logic gates have?

  Two inputs and one output

  
• What are the two binary conditions represented by logic gates?

  Low (0) and high (1)
• What are the main types of logic gates mentioned?

  AND, OR, NOT, NAND, NOR, XOR, and XNOR gates
• What is the function of an AND gate?

  • Outputs logic 1 only when all inputs are logic 1
  • Outputs logic 0 otherwise
• How is the AND operation represented?

  With a dot (.) or sometimes omitted
• What does the truth table for an AND gate look like?

  • A = 0, B = 0 → Y = 0
  • A = 0, B = 1 → Y = 0
  • A = 1, B = 0 → Y = 0
  • A = 1, B = 1 → Y = 1
• What is the function of an OR gate?

  • Outputs logic 1 when one or more inputs are logic 1
  • Outputs logic 0 only when all inputs are logic 0

  
• How is the OR operation represented?

  With a plus (+)
• What does the truth table for an OR gate look like?

  • A = 0, B = 0 → Y = 0
  • A = 0, B = 1 → Y = 1
  • A = 1, B = 0 → Y = 1
  • A = 1, B = 1 → Y = 1
• What is the function of a NOT gate?

  • Produces an inverted version of the input
  • Outputs logic 0 when input is logic 1 and vice versa

  
• What is another name for a NOT gate?

  Inverter
• What does the truth table for a NOT gate look like?

  • A = 0 → Y = 1
  • A = 1 → Y = 0

  
• What is the function of a NAND gate?

  • Outputs logic 1 if at least one input is logic 0
  • Outputs logic 0 only if all inputs are logic 1

  
• How is the NAND operation represented?

  With an AND gate symbol and a small circle on the output

  
• What does the truth table for a NAND gate look like?

  • A = 0, B = 0 → Y = 1
  • A = 0, B = 1 → Y = 1
  • A = 1, B = 0 → Y = 1
  • A = 1, B = 1 → Y = 0
• What is the function of a NOR gate?

  • Outputs logic 1 if all inputs are logic 0
  • Outputs logic 0 if any input is logic 1
• How is the NOR operation represented?

  With an OR gate symbol and a small circle on the output

  
• What does the truth table for a NOR gate look like?

  • A = 0, B = 0 → Y = 1
  • A = 0, B = 1 → Y = 0
  • A = 1, B = 0 → Y = 0
  • A = 1, B = 1 → Y = 0
• What is the function of an XOR gate?

  • Outputs logic 1 if either input is high, but not both
• How is the XOR operation represented?

  With an encircled plus sign
• What does the truth table for an XOR gate look like?

  • A = 0, B = 0 → Output = 0
  • A = 0, B = 1 → Output = 1
  • A = 1, B = 0 → Output = 1
  • A = 1, B = 1 → Output = 0
• What is the function of an XNOR gate?

  • Outputs logic 1 if both inputs are the same
  • Outputs logic 0 if inputs are different
• How is the XNOR operation represented?

  With an XOR gate symbol and a small circle on the output
• What does the truth table for an XNOR gate look like?

  • A = 0, B = 0 → Output = 1
  • A = 0, B = 1 → Output = 0
  • A = 1, B = 0 → Output = 0
  • A = 1, B = 1 → Output = 1
• What is Boolean algebra also referred to as?

  Boolean Logic or just Logic
• Who proposed Boolean algebra and when?

  George Boole in 1847
• What is the purpose of Boolean algebra?

  • To facilitate the analysis and design of digital circuits
  • Fundamental to software and hardware operations
• What are Boolean variables?

  • Take values of either 0 or 1
  • Represented by symbols like A, B, C, etc.

  
• What are the five logic operations commonly used in Boolean algebra?

  • AND
  • OR
  • NOT
  • NAND
  • NOR
• What is a Boolean function?

  • A mathematical function that derives Boolean output from Boolean inputs
  • Defined over the Boolean domain {0, 1}
• What is a Boolean expression?

  • A combination of Boolean constants, variables, and logical connectives
  • Always produces a Boolean value
• What is a truth table?

  • A table that shows all possible input combinations and their corresponding outputs
  • Used to represent the switching function of a logic gate or circuit

  
• How many possible input combinations does a 2-input logic gate have?


  • Four possible combinations: (0, 0), (0, 1), (1, 0), (1, 1)
• How many possible input combinations does a logic circuit with n inputs have?

  • 2$^n$ possible combinations
• What is the relationship between a Boolean function and its binary variables?

  • Can be represented in a truth table showing all possible input conditions

  
• What is the process for creating a truth table for a Boolean function?

  1. List all input variables
  2. Fill in binary counts for all combinations
  3. Add columns for intermediate results

  
• How many possible input combinations does a 3-input logic circuit have?

  8
• What is the formula for calculating the number of possible input combinations for a logic circuit with "n" inputs?

  2$^n$
• How many possible input combinations does a 4-input logic circuit have?

  16