Link? I must find out how to calculate a square root using a checker board!
This is a bi-quinary calculator. It is similar to Roman numerals, except that placing a 1 to the left of a 5 does not work.
Each row is a register. It contains one number.
Use some kind of marker to locate the decimal point for each register..
Use another kind of marker for the carat for finding the multiply/divide decimal.
Each digit (square) has up to 4 counters in the space and one counter on the line to the left (and slightly up) to indicate 5.
The four arithmetic functions on an abacus or counting board are elementary.
Long division can be accomplished by alternately using two registers for the partial products.
Decimal point placement is the same as in normal arithmetic.
The square root is taken using Newton's method of approximation.
Place the decimal point as far left as the original number needs space to fit in. Digits to the right of the decimal point are the accuracy of the result.
1. Make an initial guess.
2. Divide the original number by the guess
3. Add the quotient to the guess
4. Divide the sum by two
5. If the result is equal (or close enough for your purpose) to the guess, then stop. You have the answer.
6. Copy the result into the guess register as the new guess and repeat steps 2 thru 6.
Note that steps 3 and 4 are averaging the guess with the original number divided by the guess.
With the counting board/checkerboard, you need these registers (rows on the checkerboard):
Original number
Guess
Two partial quotient registers (part of the long division process.)
Quotient/sum/result (the addition and division by two can occur in the same register).
You can get double precision (and longer calculation times) by putting two checkerboards side by side.