# Disk Operating System/Numeral System

## Objective

• Learn different numeral systems used in computing.
• Learn which numeral system to use when computing.
• Learn how to do basic arithmetic operations in each numeral system.

## Numeral System

### The Binary Numeral System

This is as low as a numeral system can get. In this system of, the numeral system is 2 based, so we use Arabic numerals 0 and 1. To declare a number as binary, you usually append a postfix b or 2 at the end of the number so you could write 1010112 or 101011b. You don't necessarily need to append these at the end of a binary number, but it helps people not to confuse the number with a different numeral system, like the Decimal numeral system. This numeral system can be used when working with computers, but it tends to get long (Ex: 11111010011011002 is 64108).

Since binary is 2 based, the maximum value in each position in the number is 1, so 12+12=102 and 102+112=1012. Subtraction follows the same rules as addition, 1112-12=1102 and 1002-112=12.

### The Octal Numeral System

The octalnumeral system has been used by some cultures around the world, but it has only be significantly used in computing. Since computer's back in the day used a 8 based computing system, using this 8 based numeral system was a good idea at the time. Computer architecture has changed since then and octal is mostly obsolete on x86 computers, but it still is used occasionally. We use the Arabic numerals 0-7 to display the octal numbers. Octal uses the postfix 8 or o and you could append a prefix 0o or qo. You don't necessarily need to append these at the end of a binary number, but it helps people not to confuse the number with a different numeral system, like the Decimal numeral system. Since this numeral type doesn't work great on the x86 architecture, you should probably refrain from using it.

Since octal is 8 based, the maximum value in each position in the number is 7, so 78+18=108 and 238+78=328. Subtraction follows the same rules as addition, 108-18=78 and 438-178=248.

### The Decimal Numeral System

This is by far the most commonly used numeral system in the world. This system of counting is 10 based. In European speaking countries, and a lot of others countries, we use the Arabic numerals 0-9 to display numbers. This isn't the best numeral system to use when working with computers, but it is easy for humans to work with.

Since decimal is 10 based, the maximum value in each position in the number is 9, so 9+9=18 and 10+11=21. Subtraction follows the same rules as addition, 10-1=9 and 23-8=15. I hope that you have some for of education in mathematics, since this numeral system is most commonly taught world-wide. Completion status: Been started, but most of the work is still to be done.