Binary Abacus Information Site

the Moonstick Co.'s first "usable" binary abacus

a preliminary copy of binary abacus instructions
including a proposed notation for writing binary numbers

extracting the square root of ½ ()
on a binary abacus

Larger bits are to the right. If the 1st, 2nd, 3rd, and 4th rows of the
abacus are referred to as registers A, B, C, and D respectively, then notice that
during the first part of the calculation it is always true that A-B+C²=½.
The calculation begins with A=**½** and all other registers
empty and aims to arrive at a state where C=
with all other registers empty. During a later part of the calculation there
is insufficient precision (only 32 bits) to maintain exact equality (A-B+C²=½),
so register D begins to accumulate an upperbound on the error and thereafter it
is true that ½<A-B+C²<½+D. One can see at the very
end that there is insufficient information to determine whether the 30th bit is
up or down. To follow this more closely you can look
at it frame by frame.