Binary Encoders, Decoders and Adders

• Circuit design employs binary encoders and decoders.

Binary Encoder

• Converts multiple input lines into fewer output lines.
• An example is converting 8 input lines into 3 output bits.
• Compresses information.

Binary Decoder

• Converts fewer input bits into multiple output lines
• An example is converting 3 input bits into 8 output lines.
• Acts as an expansion of information.
• Selects memory locations or activates devices.

Binary Arithmetic

• Includes addition, subtraction, multiplication, and division in base-2.
• Requires practice in number conversion as well as arithmetic
• Numbers should line up accurately as in normal math.
• Carry-over occurs when 1+1 = 10 in binary.

Binary Adders and Subtractors

• Half Adder: Adds 2 bits, providing Sum and Carry outputs.
• Full Adder: Adds 3 bits (2 inputs + carry-in), outputting Sum and Carry.
• Subtractor: Performs binary number subtraction and uses 2’s complement to convert subtraction into addition.

Binary Subtraction with 2's Complement

• Find 2’s complement of B to subtract A - B using addition.
• Invert all bits (1’s complement), and add 1.
• Add the result to A.
• Disregard any carry-out.
• This is preferred due to computer's ability to do all operations as addition.

Multiplexer (MUX)

• Selects one output from multiple inputs based on selector bits.
• Like a train switch selecting a track.

Demultiplexer (DEMUX)

• Routes a single input to one of many outputs using selector bits.
• Like a fountain spraying water in one direction at a time.

Basic Computer Organization

• Memory: Stores data and instructions
• CPU: Executes instructions in memory
• Input/Output Devices: Facilitate user and environment interaction
• Buses: Carry data and control signals within the machine
• Key terms include MAR, MDR, ALU, PC, and IR.

CPU Architecture

• Registers: Fast, small storage units within the CPU
• ALU: Performs arithmetic and logic operations.
• Control Unit: Oversees instruction execution.
• Instruction Cycle: Fetch → Decode → Execute → Store → Repeat

CPU Instruction Execution

• Fetch: Instruction retrieval from memory.
• Decode: Interpreting the instruction's meaning.
• Execute: Performing the instruction (e.g., adding numbers).
• Store: Saving the computed result.
• Repeat: Continues processing the next instruction.

Assembly Language

• Low-level language close to machine code
• Uses mnemonics like ADD, SUB, MOV
• Each command completes a task
• Understanding hardware instruction execution.

ARM & MIPS Assembly Language

• Two popular CPU architectures, with distinct assembly languages.
• ARM Assembly: Instructions like MOV R0, #5 and ADD R1, R0, #2.
  • Uses registers R0, R1, etc.
• MIPS Assembly: Instructions like add $t0, $t1, $t2.
  • Uses registers $t0, $t1, $s0, etc.
• Focus on: Simple arithmetic, memory load/store, and instruction format comprehension.