Computer Science Number Systems and Logic Gates

Number Systems

• Conversion between binary, hexadecimal, and octal number systems is a core concept.
• Example: (1101011)2 = (6B)16 and (1111011)2 = (173)8
• BCD (Binary Coded Decimal): Represents decimal digits using 4-bit binary.
• Excess-3: Adds 3 to each BCD digit, providing self-complementing property.
• Gray code: Each code differs from the previous by one bit, eliminating ambiguity in transitions.
• Two's Complement: Used for representing negative numbers in binary.

Logic Gates and Boolean Algebra

• Basic Gates: AND, OR, NOT
• NAND Gate is universal, meaning it can be used to build all other gates
• De Morgan's Theorems: Provide rules for simplifying Boolean expressions using NOT, AND, and OR gates:
  • NOT(A AND B) = (NOT A) OR (NOT B)
  • NOT(A OR B) = (NOT A) AND (NOT B)

Combinational Circuits

• Half Adder: Adds two single bits, producing a sum and carry.
• Full Adder: Adds three bits, using two half adders.
• K-Map (Karnaugh Map): A graphical method for simplifying Boolean expressions.
• BCD to 7-Segment Decoder: Converts BCD code to activate segments in a 7-segment display.
• Programmable Logic Array (PLA): A programmable logic device that can implement a wide range of logic functions.

Sequential Circuits

• Flip-Flops: Digital circuits that can store a bit of information. Common types are:
  • D type flip-flop: Stores the value of input D when a clock pulse arrives.
  • JK flip-flop: Stores the value of input J or K, depending on the current state.
  • Master-Slave Flip-Flop: Combines two flip-flops to prevent race conditions during clock transitions.
• Shift Registers: Circuits that shift data bits with each clock pulse. Types include:
  • Serial-in, Serial-out: Input and output data sequentially.
  • Serial-in, Parallel-out: Input data sequentially, output data in parallel.
  • Parallel-in Parallel-out: Load and output data in parallel.
• Ring Counter: A type of shift register that cycles through a sequence of states, useful for implementing counters.
• Counters: Circuits that count events using flip-flops and logic gates.

Memory

• SRAM (Static RAM): Uses latches to store data, fast but power-consuming.
• DRAM (Dynamic RAM): Uses capacitors to store data, slower but less power-consuming.
• Volatile Memory: Loses its contents when power is removed.
• Non-volatile Memory: Retains its contents even when power is removed.

Analog-to-Digital Converters (ADC)

• Dual Slope ADC: A type of ADC that uses a ramp generator and integrator to convert an analog voltage to digital.

Digital-to-Analog Converters (DAC)

• DAC 0808: A common type of IC DAC that can convert binary inputs to analog output voltages.

Other Important Concepts

• Mux (Multiplexer): Selects one of multiple input signals based on a control signal.
• TTL (Transistor-Transistor Logic): A logic family using bipolar transistors.
• CMOS (Complementary Metal-Oxide Semiconductor): A logic family using MOSFET transistors, known for low power consumption.
• Fan-In: The number of inputs a logic gate can handle without affecting its operation.
• Fan-Out: The number of outputs a logic gate can drive without affecting its operation.
• Propagation Delay: The time it takes for a signal to pass through a logic gate.

This quiz covers essential concepts in number systems, including binary, hexadecimal, and octal conversions, as well as BCD and Gray code. Additionally, it delves into the basics of logic gates, Boolean algebra, and combinational circuits like adders. Test your understanding of these fundamental computer science topics.