Binary Conversion Steps for Decimal Number

Number System Conversions

• Decimal number 2910 converts to binary 111012 through successive division by 2, yielding remainders of 1, 0, 1, 1, and 1.
• The process for converting binary 111012 back to decimal involves positional value multiplication: (1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20) equals 2910.
• Octal 258 converts to decimal by calculating ((2 × 81) + (5 × 80)), resulting in decimal 2110.
• Decimal 2110 can be converted to binary, resulting in binary 101012 using similar division steps as before.

Conversion Techniques

• Binary to octal conversion is done by grouping binary digits into sets of three (from the right) and converting each to its octal equivalent.
• Octal to binary conversion requires converting each octal digit into a three-digit binary number and combining them.
• Binary to hexadecimal involves grouping binary digits into sets of four and converting each group into a hexadecimal symbol.
• Hexadecimal to binary conversion entails converting each hexadecimal digit into a four-digit binary number.

Combinational Circuits

• Output of combinational circuits depends solely on current inputs, with no memory of previous states.
• Types of combinational circuits include adders, subtractors, decoders, encoders, multiplexers, and demultiplexers.

Half Adder

• A half-adder takes two binary inputs and provides two outputs: sum and carry.
• Logical expressions for half-adder:
  • Sum = A⊕B
  • Carry = AB
• Can be implemented using NAND or NOR gates.

Full Adder

• A full adder adds three 1-bit binary numbers (A, B, and C) with outputs for sum and carry.
• The main difference from a half-adder is the additional input.
• Requires two half-adders for implementation, utilizing nine universal gates (NAND/NOR).

Computer Components

• Komponents of a computer are divided into hardware (physical devices like CPU and storage) and software (programs like operating systems and applications).
• The functional units of a computer consist of input, memory, arithmetic logic unit (ALU), output, and control unit.

8086 Architecture

• 8086 architecture features a 16-bit ALU, 16-bit registers, segmented memory addressing, and overlapping instruction fetch and execution.
• Two main functional parts: Execution Unit (EU) and Bus Interface Unit (BIU) operate asynchronously, enhancing processing speed.

Execution Unit (EU)

• Informs the BIU of memory locations for instruction fetching and executes those instructions.
• Components include general purpose registers, ALU, flag register, instruction decoder, and control unit.
• Functions include fetching instruction opcodes, decoding, and performing arithmetic/logical operations.

Bus Interface Unit (BIU)

• Handles data and address transfer between the processor and memory/I/O.
• Computes addresses and fetches instruction codes, storing them in a FIFO register set known as the Queue register.

This quiz focuses on the process of converting the decimal number 29 into its binary equivalent using division by 2. Follow the steps outlined to understand how each division operation results in the final binary form. Test your understanding of binary conversion with this exercise.