Octal to Decimal

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Best Octal to Decimal Converter Tool

The decimal number system is the number system many of us use daily. Also referred to as denary, it is a base 10 number system, meaning it is comprised of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9.

Octal numbers, sometimes referred to as oct, are base 8 numbers. The octal number system consists of only 8 digits: 0, 1, 2, 3, 4, 5, 6 & 7.

The base 8 system is often used in computing applications because one octal digit evenly represents three binary bits, which are cleanly divisible in 6, 12, 24, and 36-bit computer systems. Since most modern computer systems are 16, 32, or 64-bit systems and these are cleanly divisible into base 16 numbers, the hexadecimal system is more commonly used today.

Decimal System

The decimal numeral system is the most commonly used and the standard system in daily life. It uses the number 10 as its base (radix). Therefore, it has 10 symbols: The numbers from 0 to 9; namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

As one of the oldest known numeral systems, the decimal numeral system has been used by many ancient civilizations. The difficulty of representing very large numbers in the decimal system was overcome by the Hindu–Arabic numeral system. The Hindu-Arabic numeral system gives positions to the digits in a number and this method works by using powers of the base 10; digits are raised to the nth power, in accordance with their position.

For instance, take the number 2345.67 in the decimal system:

The digit 5 is in the position of ones (100, which equals 1),
4 is in the position of tens (101)
3 is in the position of hundreds (102)
2 is in the position of thousands (103)

Meanwhile, the digit 6 after the decimal point is in the tenths (1/10, which is 10-1) and 7 is in the hundredths (1/100, which is 10-2) position
Thus, the number 2345.67 can also be represented as follows: (2 * 103) + (3 * 102) + (4 * 101) + (5 * 100) + (6 * 10-1) + (7 * 10-2)

The Octal System

The octal number system (or shortly oct) uses the number 8 as its base (radix). As a base-8 numeral system, it uses eight symbols: The numbers from 0 to 7, namely 0, 1, 2, 3, 4, 5, 6 and 7. Although it was used by some native American tribes until the 20th century, the octal system has become popular in the early ages of computing as a language of computer programming. This is because the octal system shortens binary by simplifying long and complex chains of binary displays used by computers.

The octal system is mainly used for counting binary in groups of three: Each octal digit represents three binary digits. Since 8 is 2 to the third power (23), the octal system became a perfect abbreviation of binary for machines that employ word sizes divisible by three - which were 6-bit, 12-bit, 24-bit or 36-bit. Nowadays, most modern systems use hexadecimal rather than octal. However, octal numbers are an important part of basic knowledge in electronics.