Suppose we wish to compute the signed binary representation U of the decimal fraction using signed binary operations, we simply evaluate
To compute this more efficiently, we observe
We can now use a simple recursive algorithm using the average and division by an integer operations which evaluates to zero on an empty input, but otherwise computes:
Because we cannot represent decimal digits in signed binary streams, we replace a in the right hand side of the expression by a stream which represents a/24, and multiply the entire result by 24. Multiplication and division by powers of two can be performed easily using shift operations.