When you need to multiply 7*8 do you simply have it memorized, or do you need to add, subtract or otherwise connect it to another math fact that you know better?
That is do you simply think "56" or are there more thoughts that lead to 56?
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@futurebird memorized long time ago in a different language, so 7x8 is instant but "seven times eight" requires extra translation.
@futurebird Six times seven is forty-two by association with Hitchhiker's Guide to the Galaxy; add fourteen to that.
(My dad used to always point out when we watched the HHGTTG TV series on Betamax that multiplying six by nine does not, in fact, make forty-two, and that actually six times seven does.)
@futurebird usually instantly. When I'm having a bad day 8²-8 since squares are burnt into my brain for some reason (and within reason, magnitude-wise)
@futurebird for whatever reason the multiples of seven (especially * 6 and * 😄 tripped me up until I forced myself to more actively try and memorize them.
* because 7 is greater than 5 most of the time when you add it to a two digit number you must carry which is another opportunity to make an error.
* it is not a multiple of 2 so you can't use counting by twos to help
* 9 is easy and there are may tricks to remember the multiples of 9s
* Therefore 7 is the most troublesome number.
@futurebird @jitterted Being a football fan when I was a kid made 7 a very easy number for me to deal with.
@futurebird @jitterted Also, 7 has a disturbing history, 7 ate 9
@futurebird 7*2=14,14*2=28,28*2=40+(8*2=16)=56 is how I get there.
@futurebird I've multiplied the single-digit numbers so many times in my head that I get 56 instantly, but when I was a kid I had an easier time remembering that 7*7 = 49 or 7*9 = 63 and then either adding or subtracting.
@futurebird personally for good and fast muscle-memory outcome=derivation based on imprinted squares.
7*7=49 +7=50+(7-1) ==56
@futurebird This is why we memorized the multiplication tables. It turns multiplication and division into O(n) problems (n = number of digits).
@futurebird Oddly, perhaps, this is the last of the "multiplication table" I memorized (though that rote memory has eroded in later years). So, for me, it was "7x4x2" for most of my educational life.
I wouldn’t be the first person to have memorized entire tables of multiplication.
Computing it is easy enough, but hash look up still works
@futurebird : Well, in spite of my math minor, and a lifetime of computer worship, I have to admit that I was never able to *completely* memorize my multiplication tables. But I can usually remember most of them. 🙄
@futurebird It's instant, but followed instantly by me checking my math to make sure it's accurate.
@futurebird I have to rely on 8=2^3 and count 14, 28, 56.
Mostly instant memory. But sometimes also `8*(8-1)` = `64 - 8`
@futurebird 7 * 8 ? This is how I do it i my head 😉
0111
1000
______ apply logical AND of each bit in multiplier to the multiplicand and shift results to match bit position in the multiplier.
---0000
--0000.
-0000..
0111... (add all these 4)
_________
0111000 = 8 + 16 + 32 =56 !
7 * 5 :
0111
0101
------
...0111
..0000.
.0111..
000...
---------
010011 = 32 + 2 + 1 = 35 !
(your question prompted search I had been meaning to do for long on how CPU multiply).