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We are most familiar with the decimal number system, which is a base-10 system. This system is natural to us because we have 10 fingers on our hands, and we use our fingers for counting. This system is based in 10 digits, zero to nine. In this system, each digit in the number represents a power of 10. The far-right digit represents the “1s” which can be thought of as 10^0. The next digit to the left represents the “10s,” which can be thought of as 10^1. As we continue to the left, the next digits represent the “hundreds” (10^2), the “thousands” (10^3), and so on.
EXAMPLE
In the decimal numbering system, the number 1010 contains four digits, and each digit corresponds to a power of 10. We can break down 1010 into four digits — 1, 0, 1, 0 — and associate each digit with its corresponding power of 10: (1 x 1000) + (0 x 100) + (1 x 10) + (0 x 1). If we add these numbers, we get the value 1010.Computers primarily use the base-two numbering system, also known as the binary number system. This system is based on two digits: 0 and 1. In this system, each digit in the number represents a power of two. The far-right digit represents the “1s” which can be thought of as 2^0. The next digit to the left represents the “2s” which can be thought of as 2^1. As we continue to the left, the next digits represent the “fours” (2^2), the “eights” (2^3), and so on.
EXAMPLE
In the binary number system, the number 1010 contains four digits, and each digit corresponds to a power of two. We can break down 1010 into the four digits — 1, 0, 1, 0 — and associate each digit with its corresponding power of two: (1 x 8) + (0 x 4) + (1 x 2) + (0 x 1). In base-10, this evaluates to 10.The octal number system is based on eight digits (zero through seven). In this system, each digit in the number represents a power of eight. The far-right digit represents the “1s” (8^0). The next digit to the left represents the “eights” (8^1). As we continue to the left, the next digits represent 8^2 (which is 64), 8^3 (which is 512), and so on.
EXAMPLE
In the octal numbering system, the number 1010 contains four digits, and each digit corresponds to a power of eight. We can break down 1010 into the four digits — 1, 0, 1, 0 — and associate each digit with its corresponding power of eight: (1 x 512) + (0 x 64) + (1 x 8) + (0 x 1). In base-10, this evaluates to 520.Computers also use a hexadecimal number system for some tasks, such as defining color. Hexadecimal is a numbering system based on 16 digits (hex meaning six, and decimal meaning 10). The first 10 digits are the numbers zero through nine, and because we don’t have any single digit numbers to represent 10 through 16, we use the first six letters of the alphabet, A through F. In this system, each digit in the number represents a power of 16. The far-right digit represents the “1s” (16^0). The next digit to the left represents the “16s” (16^1). As we continue to the left, the next digits represent 16^2 (which is 256), 16^3, (which is 4096), and so on.
EXAMPLE
In the hexadecimal numbering system, the number 1010 contains four digits, and each digit corresponds to a power of 16. We can break down 1010 into the four digits — 1, 0, 1, 0 — and associate each digit with its corresponding power of 16: (1 x 4096) + (0 x 256) + (1 x 16) + (0 x 1). In base-10, this evaluates to 4112.Source: Derived from “Information Systems for Business and Beyond” by David T. Bourgeois. Some sections removed for brevity. https://www.saylor.org/site/textbooks/Information%20Systems%20for%20Business%20and%20Beyond/Textbook.html#_Chapter2:_What
