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Welcome to NRICH.

Bases of numbers

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By Arun Iyer on Tuesday, November 06, 2001 - 06:16 pm:

Can anyone explain to me what a "number in base a" means?

love arun

By Dan Goodman on Tuesday, November 06, 2001 - 09:35 pm:

Yup. For example, if a=10 then this is the normal way of writing a number: if the digits (in base 10) are d_nd_n-1d_n-2...d₂d₁d ₀ then this represents the number 10ⁿd_n+10^n-1d_n-1+...+100d ₂+10d₁+d₀ where each d_i is between 0 and 9 inclusive. Writing a number in base a means you have digits d_n to d₀ each between 0 and a-1 and the number represented is aⁿd_n+...+d₀. For example, in base 4 the number 103 means 3+4*0+4²*1=3+16=19. In base 7 the number 216 means 6+7*1+49*2=111 (if my arithmetic is OK). Let me know if that explains it.

By Arun Iyer on Wednesday, November 07, 2001 - 05:38 pm:

I got you Dan!!!
One more thing.....does it have to do anything with the log......?

love arun

By Dan Goodman on Wednesday, November 07, 2001 - 10:24 pm:

Not sure if there is much relation between this and log. The connection might be that log_a is the inverse of a^x and a is called the base of a^x or of log. Writing numbers in base a you have terms that look like d_naⁿ so you have a being the base of aⁿ. That's all.

By Arun Iyer on Friday, November 09, 2001 - 07:03 pm:

Yup i got ya!!!

thanks Dan

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