Why does base 62: zzzz = base 10: 14,776,336?

[TheArium]

I watched this Tech Quickie 

 

I've never been introduced to alphanumerical counting and the logics of binary codes before, but I think I get the system.

 

However, early in the video it is stated that when you have a binary code, each new digit must be worth twice as much as the last digit, 1, 2, 4, 8, 16, 32 etc. Just like when you have a decimal number each new digit is 10 times larger than the last; 1, 10, 100.

 

I get that. Following that logic binary 10011011 equals decimal 155. No problem there, the video explains why in a perfectly understandable way. (1*128+0*64+0*32+1*16+1*8+0*4+1*2+1*1=155).

 

But then he goes further into the alphanumerical systems, explaining that you can get to base 62 using 0-9 and all letters both capital and non-capital. Now comes the part I don't get. The video states that base 62 "zzzz" equals base 10 "14,776,336", but 62^4=14,776,336 - how about the other z's?

 

The calculation above shows how zeros result in the value to witch it applies being equal 0 zero, naturally. That's binary, but wouldn't that count in any base system as well? 0 multiplies by 0, meaning the value is 0. So in order to write 14,776,336 in base 62 you should write "z000" because, reading from right to left, you have (62*0 + 0*3844 + 0*238,328 + 1*14,776,336).

 

62^1=62

62^2=3844

62^3=238,328

62^4=14,776,336

 

Okay, as I write this I realize something is off but I'm starting to confuse myself trying to convert all this stuff into decimals in my head so I'll leave this to someone who knows how it works.

 

I hope you get what I'm trying to explain.

 

I don't know if I'm in the right subforum.

[MrSuperb]

zzzz base 62 is

61*62^3 + 61*62^2 + 61*62^1 + 61*62^0 = 14 776 335 in decimal

 

 

10011011 base 2 is

1*2^7 + 0*2^6 + 0*2^5 + 1*2^4 + 1*2^3+ 0*2^2 + 1*2^1 + 1*2^0 = 155 in decimal

[MrSuperb]

 

But then he goes further into the alphanumerical systems, explaining that you can get to base 62 using 0-9 and all letters both capital and non-capital. Now comes the part I don't get. The video states that base 62 "zzzz" equals base 10 "14,776,336", but 62^4=14,776,336 - how about the other z's?

 

The calculation above shows how zeros result in the value to witch it applies being equal 0 zero, naturally. That's binary, but wouldn't that count in any base system as well? 0 multiplies by 0, meaning the value is 0. So in order to write 14,776,336 in base 62 you should write "z000" because, reading from right to left, you have (62*0 + 0*3844 + 0*238,328 + 1*14,776,336).

 

 

14 776 336 in base 62 is actually "10000"

1*62^4 + 0*62^3 + 0*62^2 + 0*62^1 + 0*62^0

 

 

zzzz in base62 is 14 776 335 in decimal, but you still have the "0", so in both cases you have 14 776 336 combinations.

base 62: 0,1,2,3,.....,9,A,B,......,Y,Z,a,b,...,z,10,11,12,....,19,1A,1B,.....

base 10: 0,1,2,3,....,9,10,11,...