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The first few steps of the reflect-and-prefix method. 4-bit Gray code permutation. The binary-reflected Gray code list for n bits can be generated recursively from the list for n − 1 bits by reflecting the list (i.e. listing the entries in reverse order), prefixing the entries in the original list with a binary 0, prefixing the entries in the ...
The reason for adding 6 is that there are 16 possible 4-bit BCD values (since 2 4 = 16), but only 10 values are valid (0000 through 1001). For example: 1001 + 1000 = 10001 9 + 8 = 17 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.
The 5-bit Baudot code used in early synchronous multiplexing telegraphs can be seen as an offset-1 (excess-1) reflected binary (Gray) code. One historically prominent example of offset-64 (excess-64) notation was in the floating point (exponential) notation in the IBM System/360 and System/370 generations of computers.
The binary digits are grouped by threes, starting from the least significant bit and proceeding to the left and to the right. Add leading zeroes (or trailing zeroes to the right of decimal point) to fill out the last group of three if necessary. Then replace each trio with the equivalent octal digit. For instance, convert binary 1010111100 to ...
Gillham code is a zero-padded 12-bit binary code using a parallel nine-[1] to eleven-wire interface, [2] the Gillham interface, that is used to transmit uncorrected barometric altitude between an encoding altimeter or analog air data computer and a digital transponder.
Aiken code (symmetry property) Aiken code in hexadecimal coding. The following weighting is obtained for the Aiken code: 2-4-2-1. One might think that double codes are possible for a number, for example 1011 and 0101 could represent 5. However, here one makes sure that the digits 0 to 4 are mirror image complementary to the numbers 5 to 9.
Examples of six-bit binary codes are: International Telegraph Alphabet No. 4 [4] Six-bit BCD (Binary Coded Decimal), used by early mainframe computers. Six-bit ASCII subset of the primitive seven-bit ASCII; Braille – Braille characters are represented using six dot positions, arranged in a rectangle. Each position may contain a raised dot or ...
Biased codes (and Gray codes) are non-weighted codes. In excess-3 code, numbers are represented as decimal digits, and each digit is represented by four bits as the digit value plus 3 (the "excess" amount): The smallest binary number represents the smallest value (0 − excess).