My nine-year-old has been playing with our prototype four-bit adder quite a lot. After getting bored with adding, he figured out how to do subtraction with it. Of course we talked about how to do subtraction earlier. What he ended up doing is taking a pair of numbers (x,y). Finding the two’s complement representation of -y (on his own, not using the machine), and then feeding x and -y through the machine. After playing with that for a while, he told me that he had also figured out how to multiply with it. To multiply x and y, simply feed x through the machine y times, or feed y through the machine x times. Despite Keith Devlin‘s insistence that multiplication is not just repeated addition, this works (though to be fair to Devlin, he frankly admits that it works). My son keeps asking about making a multiplier. I’ve been trying to explain to him that we will be implementing multiplication in software. I’m not sure that he gets it yet, but once we get that far his experiments should help him see how to do it.
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