Encoders, Decoders, Binary Arithmetic

• An encoder converts multiple inputs into fewer output lines, for example, 8 input lines into 3 output bits.
• A decoder converts fewer input bits into multiple output lines, activating one specific output line. For example, 3 input bits into 8 output lines.
• Encoders and decoders are used in selecting memory locations or activating specific devices in a system.
• An encoder compresses information, while a decoder expands information.

Binary Arithmetic Operations

• Binary arithmetic operations include addition, subtraction, multiplication, and division, all performed in base-2.
• When performing binary addition and subtraction, numbers should be lined up as in normal mathematics.
• In binary addition, a carry-over occurs when 1 + 1 = 10 (binary for 2).

Binary Adders and Subtractors

• A half adder adds 2 bits, producing a Sum and Carry.
• A full adder adds 3 bits (2 inputs + carry-in), producing a Sum and Carry.
• A subtractor subtracts one binary number from another.
• Subtraction can be performed using 2’s complement to turn it into addition.

Binary Subtraction using 2's Complement

• To subtract A - B using the 2's complement method, first find the 2’s complement of B.
• This involves inverting all bits of B (1’s complement) and then adding 1.
• Add the 2’s complement of B to A.
• Ignore any carry-out.
• Computers use this method to perform all operations as addition.

Multiplexer (MUX) and Demultiplexer (DEMUX)

• A multiplexer (MUX) selects 1 output from many inputs based on selector bits.
• A demultiplexer (DEMUX) routes 1 input to one of many outputs using selector bits.
• A MUX is like a train switch selecting a track, while a DEMUX is like a fountain spraying water in one direction at a time.

Basic Computer Organization

• Memory stores data and instructions.
• The CPU executes instructions.
• Input/Output Devices facilitate interaction with the user and the environment.
• Buses carry data and control signals.
• Key terms include MAR (Memory Address Register), MDR (Memory Data Register), ALU (Arithmetic Logic Unit), PC (Program Counter), and IR (Instruction Register).

CPU Architecture

• Registers are small, fast storage locations within the CPU.
• The ALU performs arithmetic and logic operations.
• The Control Unit manages instruction execution.
• The instruction cycle consists of Fetch, Decode, Execute, and Store, and then repeats.

CPU Instruction Execution

• Fetch: Retrieve the instruction from memory.
• Decode: Understand the instruction's meaning.
• Execute: Carry out the instruction (e.g., add two numbers).
• Store: Save the result.
• This process repeats with the next instruction.

Assembly Language

• Assembly Language is a low-level language close to machine code.
• Each instruction performs a specific task.
• It uses mnemonics such as ADD, SUB, MOV, etc.
• Assembly language helps in understanding how hardware runs instructions.

ARM & MIPS Assembly Language

• ARM and MIPS are popular CPU architectures with their own assembly languages.
• ARM Assembly uses instructions like MOV R0, #5, ADD R1, R0, #2 and registers R0, R1, etc.
• MIPS Assembly uses instructions like add $t0, $t1, $t2 and registers $t0, $t1, $s0, etc.
• Understand how to perform simple arithmetic, load and store values from memory, and the instruction format.