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It is defined by indexing the elements of the sequence by the numbers from to , representing each of these numbers by its binary representation (padded to have length exactly ), and mapping each item to the item whose representation has the same bits in the reversed order.
This is a list of some binary codes that are (or have been) used to represent text as a sequence of binary digits "0" and "1". Fixed-width binary codes use a set number of bits to represent each character in the text, while in variable-width binary codes, the number of bits may vary from character to character.
In a Sinclair BASIC program numeric constants are stored as ASCII followed by a 0x0E byte and a 5-byte binary floating point representation. When listing a BASIC program only the ASCII part is used but at runtime only the binary representation is used. Some Spectrum programs exploited this to obfuscate numbers, while others did so to save ...
For example, the capital letter A is represented in 7 bits as 100 0001 2, 0x41 (101 8) , the numeral 2 is 011 0010 2 0x32 (62 8), the character } is 111 1101 2 0x7D (175 8), and the Control character RETURN is 000 1101 2 0x0D (15 8). In contrast, most computers store data in memory organized in eight-bit bytes. Files that contain machine ...
The most significant digit is an exception to this: for an n-bit Gray code, the most significant digit follows the pattern 2 n-1 on, 2 n-1 off, which is the same (cyclic) sequence of values as for the second-most significant digit, but shifted forwards 2 n-2 places. The four-bit version of this is shown below:
A letter has two punches (zone [12,11,0] + digit [1–9]); most special characters have two or three punches (zone [12,11,0,or none] + digit [2–7] + 8). The BCD code is the adaptation of the punched card code to a six-bit binary code by encoding the digit rows (nine rows, plus unpunched) into the low four bits, and the zone rows (three rows ...
The modern binary number system, the basis for binary code, is an invention by Gottfried Leibniz in 1689 and appears in his article Explication de l'Arithmétique Binaire (English: Explanation of the Binary Arithmetic) which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern ...
A bitwise AND is a binary operation that takes two equal-length binary representations and performs the logical AND operation on each pair of the corresponding bits. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0).