FREE EDUCATIONAL SOFTWARE NUMBER SYSTEM BINARY, OCTAL, DECIMAL, HEXADECIMAL CONVERSION

Features:

The Number System is a Free mathematics software for performing basic arithmetic operations and conversions on different number systems namely Binary, Octal, Decimal and Hexadecimal. 

How to start with Number System software ?

• Open Genius Maker software and click "Number System" button. It opens the Number System window as shown above.
• It shows 4 calculators namely Binary (base 2), Octal (base 8), Decimal (base 10) and Hexadecimal (base 16). You may note that, each calculator show only buttons which are relevant to that number system.
• At the bottom panel you can see a set of common arithmetic operators for addition, subtraction, division and multiplication. The "C" button is meant for "Clear all" and the "CE" button is meant for "Clear Error" as in the case of any calculator. Please note that these operators are common for all number systems. 

EXAMPLE: 1

• Let us take an example.
• Click " C " button from the common operators box to clear of any existing calculation.
• Click the Buttons "1" and "2" in the Decimal system calculator.
• You will be seeing the following changes.
  •  Decimal system calculator displays "  12  "
  •  Binary system calculator displays "  1100  "
  •  Octal system calculator displays "  14  "
  •  Hexadecimal system calculator displays "  C  "
• It implies the following.
  • The number 12 in decimal system is equal to number 1100 in binary.
  • The number 12 in decimal system is equal to number 14 in octal.
  • The number 12 in decimal system is equal to number C in hexadecimal.

• Now press " + " button from the common operators box.

• Click the Button "5" in the Decimal system calculator.
• You will be seeing the following changes.
  •  Decimal system calculator displays "  5  "
  •  Binary system calculator displays "  101  "
  •  Octal system calculator displays "  5  "
  •  Hexadecimal system calculator displays "  5  "
• It implies the following.
  • The number 5 in decimal system is equal to number 101 in binary.
  • The number 5 in decimal system is equal to number 5 in octal.
  • The number 5 in decimal system is equal to number 5 in hexadecimal.

• Now press " = " button from the common operators box.

• You will be seeing the following changes.
  •  Decimal system calculator displays "  17  "
  •  Binary system calculator displays "  10001  "
  •  Octal system calculator displays "  21  "
  •  Hexadecimal system calculator displays "  11  "
• It implies the following.
  • The number 17 in decimal system is equal to number 10001 in binary.
  • The number 17 in decimal system is equal to number 21 in octal.
  • The number 17 in decimal system is equal to number 11 in hexadecimal.

• In brief, the meaning of operations we did just now are as follows.

  • In Decimal system,            12 + 5 = 17 

  • In Binary system,                (1100)₂ + (101)₂ = (10001)₂
  • In Octal system,                   (14)₈ + (5)₈ = (21)₈
  • In Hexadecimal system,     (C)₁₆ + (5)₁₆ = (11)₁₆

EXAMPLE: 2

• Now let us try another example.

• Click " C " button from the common operators box to clear of any existing calculation.
• Type 101 in binary by clicking the Buttons "1", "0" and "1" in the binary system calculator.
• You will be seeing the following changes.
  •  Binary system calculator displays "  101  "
  •  Octal system calculator displays "  5  "
  •  Decimal system calculator displays "  5  "
  •  Hexadecimal system calculator displays "  5  "
• It implies the following.
  • The number 101 in binary system is equal to number 5 in octal.
  • The number 101 in binary system is equal to number 5 in decimal.
  • The number 101 in binary system is equal to number 5 in hexadecimal.

• Now press " x " button from the common operators box.

• Type 110 in binary by clicking the Buttons "1", "1" and "0" in the binary system calculator.
• You will be seeing the following changes.
  •  Binary system calculator displays "  110  "
  •  Octal system calculator displays "  6  "
  •  Decimal system calculator displays "  6  "
  •  Hexadecimal system calculator displays "  6  "
• It implies the following.
  • The number 110 in binary system is equal to number 6 in octal.
  • The number 110 in binary system is equal to number 6 in decimal.
  • The number 110 in binary system is equal to number 6 in hexadecimal.

• Now press " = " button from the common operators box.

• You will be seeing the following changes.
  •  Binary system calculator displays "  11110  "
  •  Octal system calculator displays "  36  "
  •  Decimal system calculator displays "  30  "
  •  Hexadecimal system calculator displays "  1E  "
• It implies the following.
  • The number 11110 in binary system is equal to number 36 in octal.
  • The number 11110 in binary system is equal to number 30 in decimal.
  • The number 11110 in binary system is equal to number  1E  in hexadecimal.

• In brief, the meaning of operations we did just now are as follows.

  • In Binary system,                (101)₂ x (110)₂ = (11110)₂

  • In Octal system,                  (5)₈ x (6)₈ = (36)₈
  • In Decimal system,             (5)₁₀ x (6)₁₀ = (30)₁₀
  • In Hexadecimal system,     (5)₁₆ x (6)₁₆ = (1E)₁₆

• Now you may try using octal and hexadecimal number system calculators by the similar procedure and see the simultaneous change in all number systems.

• Important Note: The fractional numbers are not supported and hence the division operation always rounds the result to the whole integer.