Student "edition" found at {csi dot journalspace dot com}.

Maybe I shouldn't have started this blog now, not with everything that's been going on.

For the second meeting of my Computer Architecture class during the first week of the third trimester, I started the discussion with the representations of numbers inside the computer.

I started with the conversion of numbers in base two or binary to base ten, which is easier, because each digit is just multiplied by two raised to its place in the arrangement, starting with zero.

Thus the students could rattle off mentally the conversions of four bit numbers, since they only had to deal with one, two, four and eight.

From here I also showed them how to find out the maximum value of a binary number given that it has a limit of a certain number of digits, n, which is then computed as the quantity two raised to n minus one.

Converting from decimal to binary was a little trickier.

I showed the students that they had to divide the number by two and take note of the remainder, then divide that quotient and so on until they ended up with zero remainder one, which is always the last number.

Then the remainders, from the last two the first, would be the binary number representation of the original decimal.

So because the last remainder is the highest digit, it always has to be one.

I also showed them most of the arithmetic operations on binary numbers, starting from addition where they had to get it through their heads that one plus one is ten.

Division, I told them, the computer just performs by looking it up in a table, instead of actually calculating, so we skipped that.

Then I also showed them the conversion to hexadecimal or base sixteen, which, although faster from decimal than binary, because they divide by sixteen instead of two, was also faster from binary because each four bits in binary already represents one digit in hexadecimal.

Session 931 got a final quotient of zero remainder one. Class dismissed.