This is the third of a four part series on “pencil and paper” binary arithmetic, which I’m writing as a supplement to my binary calculator. The first article discusses binary addition; the second article discusses binary subtraction; this article discusses binary multiplication.
Example of Binary Multiplication
The pencil-and-paper method of binary multiplication is just like the pencil-and-paper method of decimal multiplication; the same algorithm applies, except binary numerals are manipulated instead. The way it works out though, binary multiplication is much simpler. The multiplier contains only 0s and 1s, so each multiplication step produces either zeros or a copy of the multiplicand. So binary multiplication is not multiplication at all — it’s just repeated binary addition!
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Today is the 100th day of school at my son’s elementary school. I’ve had my binary influence on prior 100th day projects, and this year was to be no different. But alas, his class is not doing one this year. I didn’t want to waste the acorn tops we saved though, so I made my own 100th day project (well not quite — I didn’t glue them):
A Binary Multiplication Problem Expressed With One Hundred Acorn Tops.
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This is the second of a four part series on “pencil and paper” binary arithmetic, which I’m writing as a supplement to my binary calculator. The first article discusses binary addition; this article discusses binary subtraction.
Example of Binary Subtraction
The pencil-and-paper method of binary subtraction is just like the pencil-and-paper method of decimal subtraction you learned in elementary school. Instead of manipulating decimal numerals, however, you manipulate binary numerals, according to a basic set of rules or “facts.”
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I’m reading Steve Wozniak’s 2006 book “iWoz” and this line got me wondering about my own Apple II:
“In every speech I give, I talk to people who are still running Apple IIs, and they say those machines are still running after this many years.”
So I got it out of the attic and powered it up. The dozen or so dead keys notwithstanding, it still works — after 30 years!
Some BASIC Commands I Tried On My Keyboard-Challenged But Otherwise Still Working Apple II
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