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A comprehensive guide on number conversion systems, including decimal, binary, octal, and hexadecimal systems. ​

INTRODUCTION

  • Introduces four basic number systems: Decimal, Binary, Octal, and Hexadecimal. ​
  • Each system has a specific base and set of symbols. ​

DECIMAL TO BINARY ​

  • Two methods for conversion: Sum-of-Weights and Repeated Division-by-2. ​
  • Example: 43 in decimal converts to 101011 in binary. ​

BINARY TO DECIMAL ​

  • Multiply each bit by 2 raised to its position index. ​
  • Example: 101011 in binary equals 43 in decimal. ​

OCTAL TO DECIMAL ​

  • Multiply each digit by 8 raised to its position index. ​
  • Example: 724 in octal equals 468 in decimal. ​

DECIMAL TO OCTAL ​

  • Divide the decimal number by 8 and track remainders. ​
  • Example: 1234 in decimal converts to 2322 in octal. ​

DECIMAL TO HEXADECIMAL ​

  • Divide the decimal number by 16 and track remainders. ​
  • Example: 1234 in decimal converts to 4D2 in hexadecimal. ​

HEXADECIMAL TO DECIMAL ​

  • Multiply each digit by 16 raised to its position index.
  • Example: ABC in hexadecimal equals 2748 in decimal. ​

OCTAL TO BINARY ​

  • Convert each octal digit to its 3-bit binary equivalent. ​
  • Example: 705 in octal converts to 111000101 in binary. ​

HEXADECIMAL TO BINARY ​

  • Convert each hexadecimal digit to its 4-bit binary equivalent. ​
  • Example: 10AF in hexadecimal converts to 0001000010101111 in binary. ​

OCTAL TO HEXADECIMAL ​

  • Use binary as an intermediary for conversion.
  • Example: 1076 in octal converts to 23E in hexadecimal. ​

HEXADECIMAL TO OCTAL ​

  • Use binary as an intermediary for conversion.
  • Example: 1F0C in hexadecimal converts to 17414 in octal. ​

BINARY TO HEXADECIMAL ​

  • Group binary bits in fours and convert to hexadecimal. ​
  • Example: 1010111011 in binary equals 2BB in hexadecimal. ​

BINARY TO OCTAL ​

  • Group binary bits in threes and convert to octal. ​
  • Example: 1011010111 in binary equals 1327 in octal. ​

Conversion System – Lesson 3

Engineering Institute of Technology