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Hexadecimal and decimal number systems are two commonly used number systems in computing and mathematics. Both systems have their own specific applications and use cases, and the ability to convert between the two is an essential skill for anyone working in these fields.
The decimal system, also known as the base-10 or denary system, is the most widely used number system in the world. It is a positional system in which each digit in a number represents a tenfold value of its position. The decimal system uses the digits 0 through 9.
The hexadecimal system, also known as the base-16 system, is primarily used in computing, including for encoding color values in web design, representing binary data in a more readable way, and for addressing memory locations. The hexadecimal system uses sixteen symbols to represent numbers: the digits 0 through 9, followed by the letters A through F, which respectively represent the values 10 through 15.
Converting from decimal to hexadecimal starts with dividing the decimal number by 16. The remainder is the least significant digit (the right-hand side) of the hexadecimal number. This process is then repeated with the quotient, until it is 0. The remainders, read in reverse order, form the equivalent in the hexadecimal system.
Converting from hexadecimal to decimal is achieved by multiplying each digit in the hexadecimal number by 16 to the power of its position (with the rightmost position being 0), and then adding up all the results.
Decimal to Hexadecimal: --------------------------- 1. Divide the decimal number by 16. 2. Note the remainder (0-9 or A-F, depending on the number). 3. Divide the result again by 16. 4. Repeat the steps until the result is 0. 5. The hexadecimal number is the sequence of remainders, read from bottom to top. Hexadecimal to Decimal: --------------------------- 1. Start on the right side of the hexadecimal number. 2. Multiply the hexadecimal digit by 16 to the power of its position. 3. Add up all the results. 4. The result is the decimal equivalent of the hexadecimal number.
The ability to convert between decimal and hexadecimal systems can be greatly beneficial for programmers, mathematicians, and web designers.