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The following charts show the numeric values of BCD characters in hexadecimal (base-16) notation, as that most clearly reflects the structure of 4-bit binary coded decimal, plus two extra bits. For example, the code for 'A', in row 3x and column x1, is hexadecimal 31, or binary '11 0001'.
BCD takes advantage of the fact that any one decimal numeral can be represented by a four-bit pattern. An obvious way of encoding digits is Natural BCD (NBCD), where each decimal digit is represented by its corresponding four-bit binary value, as shown in the following table.
The binary-coded decimal (BCD) 0 to 9 digit values require four binary bits to hold their values. Since four bits (2 4 ) can hold 16 values, this means hexadecimal (hex) digits can be represented by four bits too. [ 23 ]
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".
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.
The upper nibble is ignored, and can either be zero, or the leading-nibble for the ASCII character (value 3). [2] BCD numbers are generally assumed to be stored in the lowest byte of a register, e.g. AL; operations on unpacked BCD numbers expect the least significant digit in the lowest byte of a register, e.g. AL, and the most significant ...
The increment ensures that a value of 5, incremented and left-shifted, becomes 16 (10000), thus correctly "carrying" into the next BCD digit. Essentially, the algorithm operates by doubling the BCD value on the left each iteration and adding either one or zero according to the original bit pattern.
Binary-coded decimal (BCD) is a binary encoded representation of integer values that uses a 4-bit nibble to encode decimal digits. Four binary bits can encode up to 16 distinct values; but, in BCD-encoded numbers, only ten values in each nibble are legal, and encode the decimal digits zero, through nine.