Number systems are a way of representing numerical quantities in an organized and standardized way. There are different numbering systems, each with its own rules and characteristics. In this text, we will cover the most common number systems: decimal, binary, octal and hexadecimal.
Decimal system
The decimal system is the most used and known around the world. It uses 10 symbols to represent numeric quantities: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Every ten units, the symbol changes position, forming tens, hundreds, thousands, etc.
For example, the number 1234 in the decimal system means: 1 thousand unit (1 x 1000), 2 hundreds (2 x 100), 3 tens (3 x 10) and 4 units.
Binary System
The binary system is used in electronics and information technology, as computers work with two states: on and off, represented by the numbers 1 and 0. Thus, the binary system uses only two symbols to represent numerical quantities: 0 and 1.
Number positions in the binary system follow a sequence of powers of 2, starting from the right. For example, the binary number 1011 means: 1 x 2³ (8) + 0 x 2² (0) + 1 x 2¹ (2) + 1 x 2nd (1) = 11 in decimal.
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Octal system
The octal system uses 8 symbols to represent numerical quantities: 0, 1, 2, 3, 4, 5, 6 and 7. Each position in the octal system represents a power of 8.
For example, the octal number 237 means: 2 x 8² (128) + 3 x 8¹ (24) + 7 x 8th (7) = 159 in decimal.
Hex system
The hexadecimal system uses 16 symbols to represent numerical quantities: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. The letters A through F represent the numbers 10 through 15, respectively.
The hexadecimal system is widely used in computing, mainly to represent colors. Each position in the hexadecimal system represents a power of 16.
For example, the hexadecimal number 2A7 means: 2 x 16² (768) + 10 x 16¹ (160) + 7 x 16º (7) = 935 in decimal.
In summary, numbering systems are an important tool for representing numerical quantities in an organized and standardized way. Each system has its own rules and characteristics, and it is important to understand them in order to use them efficiently in different contexts.
