## What is a Number System?

A number system is a mathematical tool that we use to represent numbers. We use a number system to write down numbers, to do arithmetic, and to solve problems. There are many different number systems, but the most common one is the base 10 number system.

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In mathematics and computing, Hexadecimal (base 16) is a numeral system with a base of 16. It uses sixteen symbols, most often the symbols 0-9 to represent values zero to nine, and A-F (or alternatively a-f) to represent values ten to fifteen. Hexadecimal numerals widely used by computer systems in programming, and the primary alternative to base 10 numerals.

A hexadecimal number written as a string of hexadecimal digits, for example “A9”. The digits are written from left to right, with the most significant digit (the digit furthest to the right) first. So “A9” is equal to 169 in decimal.

Hexadecimal notation is helpful because it is a more compact way to represent numbers than decimal notation. For example, the decimal number “10,234” can be written more compactly as “10,234 16”. This is because in hexadecimal, each digit represents four binary digits (bits), whereas in decimal, each digit represents ten binary digits.

Hexadecimal numbers can be represented in many computer systems as either a string of hexadecimal digits, or a hexadecimal number literal. A hexadecimal number literal is a number written in prefix notation with a “0x” before it. So “0xA9” is the same as “169 16

0 1 2 3 4 5 6 7 8 9 A B C D E F

10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F

20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F

30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F

40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F

50 51 52 53 54 55 56 57 58 59 5A 5B 5C 5D 5E 5F

60 61 62 63 64 65 66 67 68 69 6A 6B 6C 6D 6E 6F

70 71 72 73 74 75 76 77 78 79 7A 7B 7C 7D 7E 7F

80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F

90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F

## Conversion of Numbers in other Positional Systems to Hexadecimal Form:

binary: 101

To convert a binary number to hexadecimal, divide the number by 16 and take the remainder. Write the number as the hexadecimal equivalent of the remainder.

To convert octal to hexadecimal, divide the octal number by 16 and take the remainder.

For example, to convert the octal number 7678 to hexadecimal, divide 7678 by 16 and take the remainder:

7678 ÷ 16 = 469 remainder 12

Therefore, the hexadecimal equivalent of 7678 is 1269.

To convert a hexadecimal number to binary, divide the number by 16 and take the remainder. This will give you the first binary digit, and the process will repeat until you have the complete binary number.

For example, the hexadecimal number A7 is equal to 1010 1111 in binary. This is because A7 ÷ 16 = 5 with a remainder of 11, so the first binary digit is 1, the second is 0, the third is 1, and the fourth is 1.

To convert hexadecimal to octal, divide the hexadecimal number by 16 and then take the remainder.

• It is difficult to convert between hexadecimal and other number systems.
• Hexadecimal notation is not as widely used as other number systems.