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When the number becomes large, conversion to decimal is very tedious. However, when mapping to hexadecimal, it is trivial to regard the binary string as 4-digit groups and map each to a single hexadecimal digit. [31] This example shows the conversion of a binary number to decimal, mapping each digit to the decimal value, and adding the results.
A binary clock might use LEDs to express binary values. In this clock, each column of LEDs shows a binary-coded decimal numeral of the traditional sexagesimal time. In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually ...
That is, the value of an octal "10" is the same as a decimal "8", an octal "20" is a decimal "16", and so on. In a hexadecimal system, there are 16 digits, 0 through 9 followed, by convention, with A through F. That is, a hexadecimal "10" is the same as a decimal "16" and a hexadecimal "20" is the same as a decimal "32".
The conversion is made in two steps using binary as an intermediate base. Octal is converted to binary and then binary to hexadecimal, grouping digits by fours, which correspond each to a hexadecimal digit. For instance, convert octal 1057 to hexadecimal: To binary:
To convert a hexadecimal number into its binary equivalent, simply substitute the corresponding binary digits: 3A 16 = 0011 1010 2 E7 16 = 1110 0111 2. To convert a binary number into its hexadecimal equivalent, divide it into groups of four bits. If the number of bits isn't a multiple of four, simply insert extra 0 bits at the left (called ...
In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. [ 1 ] [ 2 ] It is also known as the shift-and-add -3 algorithm , and can be implemented using a small number of gates in computer hardware, but at the expense of high latency .
In both formats the range of possible values is identical, but they differ in how the significand c is represented. In the decimal encoding, it is encoded as a series of p decimal digits (using the densely packed decimal (DPD) encoding). This makes conversion to decimal form efficient, but requires a specialized decimal ALU to process.
Use: {{Hexadecimal|x}} where x is the decimal number to be converted to a hexadecimal. Decimals and fractions will be rounded down. Decimals and fractions will be rounded down. The number is, by default, formatted with a final subscript 16 to display the base.