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.