(12C) Square Root

12212023, 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.
101=93=65=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*109=61
10061=3963=24 The second digit of the root is 1. The root is 3.1 New group 3900 The new number is 621 3900621=3279623=2656625=2031627=1404629=775631=144633=489 The third digit of the root is 6. The root is 3.16 New group 14400 The new number is 6321 144006321=80796323=1756 17566325=4569 The root is 3.162 New group 175600 The new number is 63241 17560063241=11235963243=49116 The root is 3.1622 Group 4911600 The number is 632421 4911600632421=4279179632423=3646756632425=3014331632427=2381904632429=174947511170444632431=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 46 characters, because only up to 13 digits of the mantissa. 

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Messages In This Thread 
(12C) Square Root  Gamo  10022019, 10:23 AM
RE: (12C) Square Root  Albert Chan  10022019, 02:36 PM
RE: (12C) Square Root  Albert Chan  09282020, 05:18 PM
RE: (12C) Square Root  Albert Chan  09282020, 07:14 PM
RE: (12C) Square Root  Gamo  10032019, 02:01 AM
RE: (12C) Square Root  SlideRule  09282020, 09:45 PM
RE: (12C) Square Root  Albert Chan  06082021, 03:36 PM
RE: (12C) Square Root  depor  12212023 11:50 PM
RE: (12C) Square Root  Dave Hicks  12232023, 01:48 AM
RE: (12C) Square Root  Thomas Klemm  12232023, 04:26 AM

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