Computer Systems: Binary Operations

• Study notes on computer systems

Binary Encoder & Decoder

• An encoder converts multiple input lines into fewer output lines
• An example is 8 input lines to 3 output bits
• A decoder takes fewer input bits and activates one specific output line
• An example is 3 input bits to 8 output lines
• Decoders are used in selecting memory locations or activating specific devices in a system
• Encoders are used for compression of information
• Decoders are used for expansion of information

Binary Arithmetic Operations

• Binary operations include addition, subtraction, multiplication, and division, all in base-2
• When performing binary arithmetic, line up numbers as normal
• In binary, carry over happens when 1 + 1 = 10 (which is 2 in decimal)
• A half adder adds 2 bits, resulting in Sum and Carry
• A full adder adds 3 bits (2 inputs + carry-in), resulting in Sum and Carry
• A subtractor subtracts one binary number from another
• 2's complement is used to turn subtraction into addition
• To subtract A - B using addition:
• Find 2's complement of B by inverting all bits (1's complement) and then adding 1
• Add the result to A
• Ignore carry-out if any
• Computers prefer to do all operations as addition

Multiplexer (MUX) and Demultiplexer (DEMUX)

• A multiplexer (MUX) chooses 1 output from many inputs based on selector bits
• A demultiplexer (DEMUX) takes 1 input and routes it to one of many outputs using selector bits
• A MUX is like a train switch selecting a track
• 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 interact with the user and environment
• Buses carry data and control signals
• Key terms:
• MAR (Memory Address Register)
• MDR (Memory Data Register)
• ALU (Arithmetic Logic Unit)
• PC (Program Counter)
• IR (Instruction Register)

CPU Architecture

• Registers are small, fast storage in CPU
• ALU performs arithmetic and logic operations
• The Control Unit manages instruction execution
• The instruction cycle repeats the following steps: Fetch, Decode, Execute, and Store

CPU Instruction Execution

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

Assembly Language

• Assembly language is a low-level language close to machine code
• Each instruction in assembly language performs a very specific task
• Assembly language uses mnemonics like ADD, SUB, MOV, etc
• Assembly language can help to understand how hardware runs instructions

ARM & MIPS 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, $t1, $t2
• Registers are $t0, $t1, $s0, etc
• Key assembly topics:
• Simple arithmetic operations
• Loading and storing values from memory
• Understanding instruction format

Final Tips

• Practice drawing simple circuits (for MUX/DEMUX, adders)
• Memorize binary addition/subtraction rules
• Try small assembly code snippets
• Know the fetch-decode-execute cycle well