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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 ...
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
Computer engineers often need to write out binary quantities, but in practice writing out a binary number such as 1001001101010001 is tedious and prone to errors. Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base-16, "hexadecimal" (hex), number format. In the decimal system, there are 10 digits, 0 ...
10001 is the binary, not decimal, representation of the desired result, but the most significant 1 (the "carry") cannot fit in a 4-bit binary number. In BCD as in decimal, there cannot exist a value greater than 9 (1001) per digit. To correct this, 6 (0110) is added to the total, and then the result is treated as two nibbles:
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:
Least significant bit first means that the least significant bit will arrive first: hence e.g. the same hexadecimal number 0x12, again 00010010 in binary representation, will arrive as the (reversed) sequence 0 1 0 0 1 0 0 0.
The octal and hexadecimal systems are often used in computing because of their ease as shorthand for binary. Every hexadecimal digit corresponds to a sequence of four binary digits, since sixteen is the fourth power of two; for example, hexadecimal 78 16 is binary 111 1000 2. Similarly, every octal digit corresponds to a unique sequence of ...
A binary encoding is inherently less efficient for conversions to or from decimal-encoded data, such as strings (ASCII, Unicode, etc.) and BCD. A binary encoding is therefore best chosen only when the data are binary rather than decimal. IBM has published some unverified performance data. [2]