Converting base b representation into decimal representation

2.4

Any integer b greater than 1 can serve as the base!

What number is (ak a k-1 ak-2 … a0)b ?

It is akbk + a k-1bk-1 + ak-2bk-2 + … + a0b0

E.g. (5032)10 = 5*103 + 0*102 + 3*101 + 2*100 =

= 5*1000 + 3*10 + 2 = 5032

(5032)8 = 5*83 + 0*82 + 3*81 + 2*80 =

= 5*512 + 3*8 + 2 = 2586

(10110)2=

1*24 + 0*23 + 1*22 + 1*21 + 0*20 =

= 16 + 0 + 4 + 2 + 0 = 22

(A3F)16 =

10*162 +

3*161+

15*160

= 2560+48+15 = 2623

Base b expansion

Base 10 expansion

Base 8 expansion

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