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For a positional numeral system of radix b, evaluating a notation $a_3 a_2 a_1 a_0$ as shown below results in decimal notation of number,

$a_3 a_2 a_1 a_0 = a_3 \times b^3 + a_2 \times b^2 + a_1 \times b^1 + a_0 \times b^0$

Why?

PS: Please keep your answers simplified

iSeeU
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1 Answers1

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You may define a numeral system in base $2b+1$ such that $$ (a_n\cdots a_2a_1a_0)=\sum a_k (2b+1)^k $$ with $-b\le a_i \le b$ (reference: Mathematics Made Difficult). This system is simpler than our usual system. You can even define Negative base.

Ma Ming
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  • Ok, Thanks for the info... But, that doesn't answer my question. Please reread it. – iSeeU Apr 22 '14 at 15:26
  • @iSeeU that is the convention, ask ancient Hindus. – Ma Ming Apr 22 '14 at 16:21
  • How can i ask them ? Can you help me with this http://math.stackexchange.com/questions/764550/if-the-role-of-a-numeral-system-is-to-provide-a-mathematical-notation-for-repres?noredirect=1#comment1589055_764550 – iSeeU Apr 22 '14 at 16:29