The Quarter square multiplier technique has also benefitted 8-bit systems that do not have any support for a hardware multiplier. Steven Judd implemented this for the [[MOS Technology 6502|6502]].<ref name=sjudd>{{Citation |last = Judd |first = Steven |date = Jan 1995 |periodical = C=Hacking |issue = 9 |url = http://www.ffd2.com/fridge/chacking/c=hacking9.txt}}</ref>
==Algorithm for multiplying numbers close to a round number==
Suppose we want to multiply two numbers <math>x</math> and <math>y</math> that are close to a round number <math>N</math>. Writing <math>x = N + x'</math> and <math>y=N+y'</math>, allows one to express the product as:
Example. Suppose we want to multiply 92 by 87. We can then take <math>N = 100</math> and implement the above formula as follows. We write the numbers below each other and next to them the amounts we have to add to get to 100:
Since the numbers on the right are <math>-x'</math> and <math>-y'</math>, the product is obtained by subtracting from the top left number the bottom right number (or subtract from the bottom left number the top right number), multiply that by 100 and add to that the product of the two numbers on the right. We have 87 - 8 = 79; 79*100 = 7900; 8*13 = 104; 7900+104 = 8004.
The multiplication of 8 by 13 could also have been done using the same method, by taking <math>N = 10</math>. The above table can then be extended to:
The product is then computed by evaluating the differences 87-8=79; 13-2 = 11, and the product 2*(-3) = -6. We then have 92*87 = 79*100 + 11*10 - 6 = 7900 + 104 = 8004.
==Fast multiplication algorithms for large inputs==
