Vedic Mathematics- Vinculum Numbers

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Cultural Computing Initiatives
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Definition:Definition:
Vinculum numbers are a mixture of positive digits and
negative digits in the same number.
Two sutras are used to convert Vinculum to Normal.
“Nikhilam navatascaramam dasatah”
“Ekanyunena purvena”
Note: Using Vinculum numbers, numbers which have digits greater than5
can be reduced to numbers which have all digits less than or
equal to 5.

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Algorithm:
Take complement of bar (negative) digits.
Subtract one from the digit preceding the bar digit(s).
Note:Only digits that have a bar on them are converted to natural
numbers.
0 =0. This can be used to make the conversion simpler,.

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Vinculum To Normal:
Find Normal No of 2 1
91
Complement of 1=9
Previous digit -1=2-1=1
Ans: 19
Sutra: “Ekanyunena purvena”
2 1

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Find Normal No of = 3 1 2
229
Next no of bar digit no change then 2=2
Complement of 1 is 9
Previous digit 3-1=2
Ans: 292
3 1 2

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Find Normal No of = 3 0 2 1
3 0 2 1
(\0 is left to a bar no extend the bar to zero also)
Complement of 02=98
Previous of 0`2 is 3,so 3-1=2
All other places are retained as they are then 1=1
Ans: 2981
19 82
3 0 2 1

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Find Normal No of = 3 4 2 1 3
69
3 4 2 1 3
213
9 is Complement of 1 & 6 is Complement of 4
Previous digits 3&2 are reduced by 1,so2&1
All other places are retained as they are then 3=3
Ans: 26193

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Normal To Vinculum
Find Vinculum No of 19
12
Here 9 is the bigger digit (Complement of 9=1 )
1 added to the previous digit then 1+1=2
Ans: 21
Sutra: “Ekadhikena Purvena “
1 9

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Find Vinculum No of 387
1 34
Complement of 87 is 13
1 added to the previous digit then 3+1=4
Ans: 413
3 8 7

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Find Vinculum No of 2917
1 332
Complement of 9&7 in their respective position
1 added to the left position of the Complement no
Ans: 3123
2 9 1 7

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Find Vinculum No of 1973
032 3
03 is complement of 97
1 added to the previous digit then 1+1=2
Other digits retained as they are 3=3
Ans: 2033
1 9 7 3

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Find Vinculum & Normal of the following numbers :
32
634
4042
23144
28
574
3962
17064
49
189
3826
2894
51
211
4234
3114
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