Not quite. Arithmetic units also do the shift, which is a crude way of multiplying by two or a power thereof.
Oddly enough, if speed is of the essence and you have the ROM space, lookup tables area very fast way to get some calculations done.
Err, what, all of them? As in every single multiplication of one digit by another, i.e. all nine for multiplying two 3-digit numbers? Blimey, how ridiculous.
Michael
Indeed, or dividing, but at a more primitive level (and a more general case) not all multiplications can be factored to powers of two. Hence why general purpose multiplication routines are much larger than specific target ones (a good reason why most screen resolutions were "powers of two" pixels wide or tall).
Yup they certainly are - even if you only cache partial or intermediate results.
but about a quarter of the size, leaving you with 5 into 46 etc. And the answer was below the original figure rather than below it. IIRC the answer only needed to go up top if the figure you were dividing by was double digit or above. We used nibs and inkwells too :-)
Which is a bit like memorising your times tables
I remember a few years ago I was after a mortgage for 50k (which will give you an idea how long ago it was). The bank manager reached for a calculator to work out how much I would need for the 5% deposit and was amazed when I worked out the correct answer in my head, after he had checked it on his calculator of course.
On the other hand though, if we have machines do the calculations it is less of an essential skill. For example being able to light a fire without matches or make an arrowhead from flint would once have been vital skills but I doubt many people could do it now. I often imagine ageing cavemen sitting around: "I gave this lad a bit of flint the other day and 'e did'n' know what t' do"
Flint was used right up to the Victorian age: Only the match really made it history, but flints are still used in cigarette lighters....
Oh no they're not!
(the so called flint in a lighter is no relation to the silicon oxide stone of the same name - its a man made metal alloy usually called ferrocerium)
Example 1
1) 3s into 3 go 1 2) 3s into 2 go 0 rem 2 3) 3s into 21 go 7Answer = 107
Example 2
1) 3s into 2 go 0 rem 2 2) 3s into 20 go 6 rem 2 3) 3s into 26 go 8 rem 2Answer = 68 rem 2
That's how I was taught, and I've never found a case where it doesn't work. You can carry on with the second example if you like. When you've reached the end of all of the numbers in the original amount that you're dividing, and are left with a remainder too small for the dividing figure to go into - i.e. the 'rem2' that we have in that example - you can then add a decimal point to the main number, and shove a few zeros after it. You then drop the decimal point down into the answer as well, then carry on dividing as you did before the point was put in there. so :
4) 206.00000 5) answer so far 68. 6) put the rem 2 after the decimal point and before your first added zero 7) 3s into .20 go 6 rem 2 8) 3s into .020 go 6 rem 2 9) 3s into .0020 go 6 rem 2And so on until you have reached the level of precision in your answer that suits the circumstances, as obviously, in this case, there is no exact answer. So the final answer arrived at here was 68.666 rec
Arfa
The ARM has a shifter in the path from registers to ALU so you can add a register to itself with a shift and do single cycle multiplies by an odd amount such as 3, 5, ... Big ARMs are dual issue so the real hardware multiplier can be doing something more meaty.
MBQ
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