Double dabble
type of algorithm
In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. It is also known as the shift-and-add-3 algorithm, and can be implemented using a small number of gates in computer hardware, but at the expense of high latency.
Algorithm
The algorithm operates as follows:
Suppose the original number to be converted is stored in a register that is n bits wide. Reserve a scratch space wide enough to hold both the original number and its BCD representation; n + 4×ceil(n/3) bits will be enough. It takes a maximum of 4 bits in binary to store each decimal digit.
Then partition the scratch space into BCD digits (on the left) and the original register (on the right). For example, if the original number to be converted is eight bits wide, the scratch space would be partitioned as follows:
Hundreds Tens Ones Original
0010 0100 0011 11110011
The diagram above shows the binary representation of 24310 in the original register, and the BCD representation of 243 on the left.
The scratch space is initialized to all zeros, and then the value to be converted is copied into the "original register" space on the right.
0000 0000 0000 11110011
The algorithm then iterates n times. On each iteration, any BCD digit which is at least 5 (0101 in binary) is incremented by 3 (0011); then the entire scratch space is left-shifted one bit.
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