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(12C) Square Root
12-21-2023, 11:50 PM
Post: #8
RE: (12C) Square Root
I will calculate quickly on a regular calculator, so that there are more numbers on the display. There is a very simple calculation algorithm that was used in Soviet Iskra (Spark) computers back in the 1970s. All that is required is the arithmetic operation of subtraction and multiplication by 10 (in essence, this is the addition of the inverse of the number and the shift registr of the left).
We divide the number into groups of 2 digits before and after the decimal point. If one digit remains, it counts as a group. Next, we use the amazing property of odd numbers — their sum is equal to the square of the number of items.
For example 1=1²; 1+3=4=2²; 1+3+5=9=3²; 1+3+5+7=16=4².

We proceed as follows - from the first group on the left, we subtract odd numbers, starting with 1.


Example.
10-1=9-3=6-5=1
The number of successful subtractions of 3 is the first digit of the root. We add the numbers of the next group.

100
We subtract odd numbers, start with the number obtained in this way — the number that gave a negative result remains, multiply by 10 and subtract 9.

7*10-9=61
100-61=39-63=-24
The second digit of the root is 1. The root is 3.1
New group 3900
The new number is 621
3900-621=3279-623=2656-625=2031-627=1404-629=775-631=144-633=-489
The third digit of the root is 6. The root is 3.16
New group 14400
The new number is 6321
14400-6321=8079-6323=1756
1756-6325=-4569
The root is 3.162
New group 175600
The new number is 63241
175600-63241=112359-63243=49116
The root is 3.1622
Group 4911600
The number is 632421
4911600-632421=4279179-632423=3646756-632425=3014331-632427=2381904-632429=1749475-11170444-632431=484611
The root is 3.1627
Group 48461100
The number is 6324321
And so on. The number of digits after the decimal point is determined by the size of the number with which the device works. For a pen and pencil, this is a lot, and for a calculator, it is 4-6 characters, because only up to 13 digits of the mantissa.
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Messages In This Thread
(12C) Square Root - Gamo - 10-02-2019, 10:23 AM
RE: (12C) Square Root - Albert Chan - 10-02-2019, 02:36 PM
RE: (12C) Square Root - Albert Chan - 09-28-2020, 05:18 PM
RE: (12C) Square Root - Albert Chan - 09-28-2020, 07:14 PM
RE: (12C) Square Root - Gamo - 10-03-2019, 02:01 AM
RE: (12C) Square Root - SlideRule - 09-28-2020, 09:45 PM
RE: (12C) Square Root - Albert Chan - 06-08-2021, 03:36 PM
RE: (12C) Square Root - depor - 12-21-2023 11:50 PM
RE: (12C) Square Root - Dave Hicks - 12-23-2023, 01:48 AM
RE: (12C) Square Root - Thomas Klemm - 12-23-2023, 04:26 AM



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