Binary Encoders, Decoders, Adders & Subtractors

Binary Encoder & Decoder (For Circuit Design)

• Encoder: Converts multiple input lines into fewer output lines, like 8 input lines to 3 output bits
• Decoder: Converts fewer input bits into one activated output line, like 3 input bits to 8 output lines
• Used for selecting memory locations or activating specific devices
• Encoder = Compression of information
• Decoder = Expansion of information

Binary Arithmetic Operations

• Binary operations include addition, subtraction, multiplication, and division, all in base-2
• Number conversion and arithmetic are used
• Numbers should be lined up appropriately
• When 1+1 happens, a carry over occurs, equaling 10 (binary for 2)

Binary Adders and Subtractors

• Half Adder: Adds 2 bits, provides a sum and carry
• Full Adder: Adds 3 bits (2 inputs + carry-in), provides a sum and carry
• Subtractor: Subtracts one binary number from another and can use 2's complement to turn subtraction into addition

Binary Subtraction using 2's Complement

• Find the 2's complement of B by inverting all bits (1's complement), then add 1
• Add this to A
• Ignore any carry-out
• Computers prefer to do all operations as addition

Multiplexer (MUX) and Demultiplexer (DEMUX)

• Multiplexer (MUX): Chooses 1 output from many inputs based on selector bits
• Demultiplexer (DEMUX): Takes 1 input and routes it to one of many outputs using selector bits
• MUX is similar to a train switch selecting a track
• DEMUX operates like a fountain spraying water in one direction at a time

Basic Computer Organization

• Memory stores data and instructions
• CPU executes instructions
• Input/Output Devices interact with the user and the environment
• Buses carry data and control signals

CPU Architecture

• Registers: Small, fast storage in the CPU
• ALU: Performs arithmetic and logic operations
• Control Unit: Manages instruction execution
• Instruction Cycle: Fetch, Decode, Execute, Store, Repeat

CPU Instruction Execution

• Fetch: Get the instruction from memory
• Decode: Understand what the instruction means
• Execute: Carry out the instruction (e.g., add two numbers)
• Store: Save the result
• Repeat: Process continues with next instruction

Assembly Language

• A low-level language close to machine code
• Each instruction is a specific task
• Uses mnemonics like ADD, SUB, MOV
• It helps one understand how hardware runs instructions

ARM & MIPS Assembly Language

• Popular CPU architectures, both with their own assembly language
• ARM Assembly: Uses instructions like MOV R0, #5, ADD R1, R0, #2.
• Registers are R0, R1, etc
• MIPS Assembly: Uses instructions like add t0,t0, t0,t1, $t2
• Registers are t0,t0, t0,t1, $s0, etc
• Need to be able to do simple arithmetic
• Need to be able to load and store values from memory
• Need to understand instruction format