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Anyone who’s handled machine code, picked out an RGB colour for a graphic or played Traveller will know about hexadecimal (base-16) numbers.

The decimal system is based on the number 10. It uses 10 digits – 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Hexadecimal is base 16, and it uses 16 digits – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 as before, but then A = 10, B – 11, C = 12, D = 13, E = 14, F = 15.

Hex numbers look strange – 30 = 48; 1666 in decimal = 682 in hexadecimal; you get numbers like 2B0CC9 (2821321 in decimal), but they are valid numbers – and you can perform Vedic mathematical calculations on them just as easily as decimals.

An example of a common Vadic procedure – squaring a number that ends in 5 by means of Ekhadikena Purvena. In the case of hexadecimal, the units digit which has the same effect as 5 is 8. The calculations are made the same way: multiply the tens digit by one more than the one before, and add the square of the units digit – in this case, 40 (64 in decimal):

282 = 640

382 = C40

982 = 5A40

What you’re doing here is multiplying 9 by the next highest digit, A (10). This yields 90, which in hexadecimal is 5A ((5 x 16) + 10).

A82 = 6E40

C82 = 9C40

F82 = F040

and so on.

This works for multiplications of the other type described in the previous post, where you are multiplying two numbers whose units digit complement one another. In this case, the pairings are 16s complements, and their digit products in hexadecimal are:-

8 x 8 = 40
7 x 9 = 3F
6 x A = 3C
5 x B = 37
4 x C = 30
3 x D = 27
2 x E = 1C
1 x F = 0F

Compare with the decimal equivalents:-

5 x 5 = 25
4 x 6 = 24
3 x 7 = 21
2 x 8 = 16
1 x 9 = 09

Let’s see some examples of this in action:-

27 x 29 = 63F

31 x 3F = C0F

42 x 4E = 141C

54 x 5C = 1E30

93 x 9D = 5A27

95 x 9B = 5A37

A1 x AF = 6E0F

D7 x D9 = B63F

F6 x FA = F03C

F5 x FB = F037

The sutra Ehadikena Purvena (By one more than the one before) works regardless of the bases, and demonstrates how truly versatile Vedic Mathematics can be.

#### 1 COMMENT

1. Honestly, I am not a mathematician. But I see the point. I as usual a doubting person, have to pick up paper and pencil to work out and understand the concepts. If your claim is true then it proves that Vedic math is NOT a freak trick but a mathematical phenomenon!
P J Naidu
jssw.india@gmail.com