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If a decimal digit requires four bits, then three decimal digits require 12 bits. However, since 2 10 (1,024) is greater than 10 3 (1,000), if three decimal digits are encoded together, only 10 bits are needed. Two such encodings are Chen–Ho encoding and densely packed decimal (DPD). The latter has the advantage that subsets of the encoding ...
In the 1960s, the term double dabble was also used for a different mental algorithm, used by programmers to convert a binary number to decimal. It is performed by reading the binary number from left to right, doubling if the next bit is zero, and doubling and adding one if the next bit is one. [5]
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. In the binary integer decimal (BID) encoding, it is encoded as a binary number.
The bits of the binary number are used one by one, starting with the most significant (leftmost) bit. Beginning with the value 0, the prior value is doubled, and the next bit is then added to produce the next value. This can be organized in a multi-column table. For example, to convert 10010101101 2 to decimal:
For instance, using a 32-bit format, 16 bits may be used for the integer and 16 for the fraction. The eight's bit is followed by the four's bit, then the two's bit, then the one's bit. The fractional bits continue the pattern set by the integer bits. The next bit is the half's bit, then the quarter's bit, then the ⅛'s bit, and so on. For example:
Densely packed decimal (DPD) is an efficient method for binary encoding decimal digits.. The traditional system of binary encoding for decimal digits, known as binary-coded decimal (BCD), uses four bits to encode each digit, resulting in significant wastage of binary data bandwidth (since four bits can store 16 states and are being used to store only 10), even when using packed BCD.
This table illustrates an example of an 8 bit signed decimal value using the two's complement method. The MSb most significant bit has a negative weight in signed integers, in this case -2 7 = -128. The other bits have positive weights. The lsb (least significant bit) has weight 2 0 =1. The signed value is in this case -128+2 = -126.
The full decimal significand is then obtained by concatenating the leading and trailing decimal digits. The 10-bit DPD to 3-digit BCD transcoding for the declets is given by the following table. b 9 … b 0 are the bits of the DPD, and d 2 … d 0 are the three BCD digits.