Number Systems and Boolean Algebra

What is a Boolean function?

• A function that outputs a string based on integer inputs.

• A function that only accepts numeric inputs.

• A function that maps binary inputs to a binary output.

• A function that maps binary inputs to decimal outputs.

Define the AND gate and its truth table.

• Truth Table for NAND Gate: | A | B | Output | | 0 | 0 | 1 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |

• Truth Table for NOT Gate: | A | Output | | 0 | 1 | | 1 | 0 |

• Truth Table for OR Gate: | A | B | Output | | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 |

• Truth Table for AND Gate: | A | B | Output | |---|---|--------| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 |

Explain De Morgan's Theorems in Boolean algebra.

• NOT (A AND B) = (NOT A) AND (NOT B)

• NOT (A OR B) = (NOT A) OR (NOT B)

• NOT (A AND B) = (A OR B)

• De Morgan's Theorems: 1) NOT (A AND B) = (NOT A) OR (NOT B); 2) NOT (A OR B) = (NOT A) AND (NOT B).

What is the binary equivalent of the decimal number 13?

• 1001

• 1101

• 1110

• 1011

How many inputs can a NAND gate have?

• One input

• Three inputs

• Two or more inputs

• Only digital inputs

What is the output of an OR gate when both inputs are false?

• undefined

• true

• null

• false

Describe the significance of the truth table in logic circuits.

• It determines the power consumption of the circuit.

• The truth table is significant in logic circuits as it provides a clear representation of how inputs relate to outputs, aiding in design and analysis.

• It is used to measure the voltage across the circuit.

• It shows the physical layout of the circuit components.

What is the hexadecimal representation of the decimal number 255?

• FF

• FE

• FF0

• F0

Explain the concept of a logic circuit.

• A logic circuit is designed to process decimal numbers for arithmetic operations.

• A logic circuit processes binary inputs through logic gates to produce a binary output.

• A logic circuit uses analog signals to produce continuous outputs.

• A logic circuit is a type of mechanical device that operates on gears.

What is the result of the Boolean expression A + A' ?

• 0

• A

• 1

• A'