Base Number Systems ~ Get Your Dream

Why 8+9 = 19, cause we talk in base 10, if we talk in base then 11+8 = 21, (cause there is no number 9 in base 9), and how its result if we talk in base 8, base 7, or may be in base 2? (we explain for next...)

Seems has become international agreement that we talk in base 10, it is number system with using 10 numbers, cause easily its logic is many numbers which we known are ten kinds, are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, so more fun communicate in base 10

Communication language actually is only an agreement in this world.
Example::

7 has been agreed be symbol to indicate something which amounts to seven, so that 7 is read by “seven”. If 8 is agreed be symbol to indicate something which amounts to seven, so that 8 is read by “seven”, then true statement is 3+4 = 8 not 3+4 = 7. And if # is agreed be symbol to indicate something which amounts to eight, so that $ is read by “seven”, then true statement is 3+4=# not 3+4=7
Why color is called by red? Why not black or yellow? Cause its agreement like that. Why color is called by green? Ya... cause be agreed like that
All this time we know symbol 9 which be agreement as a symbol indicate most in amount(nine), and to indicate amount more than nine, needed incorporation 2 symbol, example 10 is incorporation of symbol 1 and 0, and 33 is incorporation of symbol 3 and 3, etc. If A is agreed as a symbol indicate amount ten, then will be available base 11, is a numbers system using eleven numbers/symbols are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A, in which:
- 8+2=A is a true statemen, and 8+2=10 is a false statement
- 10 is a symbol indicate amount eleven, and 11 is not a symbol indicate amount eleven

Actually correct writing for base 10 numbers sequentially from
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9
are:
0₁₀, 1₁₀, 2₁₀, 3₁₀, 4₁₀, 5₁₀, 6₁₀, 7₁₀, 8₁₀, 9₁₀, 10₁₀, but also has been agreement 4₁₀ enough written by 4. Its case is same with some things follows:

enough written by
enough written by log 1000
enough written by ln a
BEGITU JUGA 4₁₀ enough written by 4

Oke, we begin the numbers system...

Numbers system base 10 (familiar with decimal)
Numbers system base 10 is numbers system using 10 numbers, are:
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9
And its writing are 0₁₀, 1₁₀, 2₁₀, 3₁₀, 4₁₀, 5₁₀, 6₁₀, 7₁₀, 8₁₀, and 9₁₀, but cause has been agreement just enough written by 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

Formula for numbers base 10:

Example:
Example for calculation in base 10:
- 3 + 5 = 8
- 6 - 12 = -7
- 4 x 9 = 36
- 21 / 7 =3
Numbers system base 9
Numbers system base 9 is numbers system using 9 numbers, are:
0, 1, 2, 3, 4, 5, 6, 7, and 8. And its writing are 0₉, 1₉, 2₉, 3₉, 4₉, 5₉, 6₉, 7₉, and 8₉
Formula for numbers base 9:

Example:
- Convert numbers 32169 to numbers base 10
- Convert numbers 2365 to numbers base 9
  First look for n value, in which result of 9ⁿ equals 2365 or greater than 2365, then gotten 9⁴ = 6561, as while 9³ = 729. So 2365 is between 9⁴ with 9³, then:
  2365 = ... x 9³ + ... x 9² + ... x 9¹ + ... x 9⁰
  If first blank is filled by number 4, its result will greater than 2365, cause
  4 x 9³ = 2916, and if first blank is filled by number 3, its result will not greater than 2365, cause
  3 x 9³ = 2187
  So gotten first blank is filled by number 3, so that:
  
  2365 = 3 x 9³ + ... x 9² + ... x 9¹ + ... x 9⁰
  If second blank is filled by number 3, its result will greater than 2365, cause
  3 x 9³ + 3 x 9² = 2430,
  And if second blank is filled by number 2, its result will not greater than 2365, cause 3 x 9³ + 2 x 9² = 2349, so that:
  
  2365 = 3 x 9² + 2 x 9¹ + ... 9⁰
  With same method like previous gotten:
  2365 = 3 x 9³ + 2 x 9² + 1 x 9¹ + 7 x 9⁰
  So, 2365 in base 10 equals 3217 in base 9, or written 2365 = 3217₉
Numbers System Base 8 (familiar with octal)
Number system base 8 is number system using 8 numbers/symbols, are:
0, 1, 2, 3, 4, 5, 6, and 7
And its writing are:
0₈, 1₈, 2₈, 3₈, 4₈, 5₈, 6₈, 7₈
Formula for number base 8:

Example:
- Convert numbers 5231₈ to base 10 numbers
- Convert numbers 2713 to numbers base 8
  With using same method like convert base 10 numbers to base 9 number, then gotten:
Numbers System Base 7 (familiar with septenary)
Number system base 7 is number system using 7 numbers/symbols, are:
0, 1, 2, 3, 4, 5, and 6.
and penulisannya adalah 0₇, 1₇, 2₇, 3₇, 4₇, 5₇, and 6₇
Formula for base 7 numbers:

Example:
- Convert numbers 1000₇ to base 10 numbers
- Convert numbers 343 to base 7 numbers
  With using same method like convert base 10 numbers to base 9 number, then gotten:
Numbers System base 6 (familiar with senary)
Number system base 6 is number system using 6 numbers/symbols, are:
0, 1, 2, 3, 4, and 5.
And its writing are 0₆, 1₆, 2₆, 3₆, 4₆, and 5₆
Formula for base 6 numbers:

Example:
- Convert numbers 3001₆ to base 10 numbers
- Convert numbers 649 to base 6 numbers
  With using same method like convert base 10 numbers to base 9 number, then gotten:
Numbers System Base 5 (familiar with quinary)
Number system base 5 is number system using 5 numbers, are:
0, 1, 2, 3, and 4.
And its writng are 0₅, 1₅, 2₅, 3₅, and 4₅
Formula for base 5 numbers:

Example:
- Convert numbers 1234₅ to base 10 numbers
- Convert numbers 194 to base 5 numbers
  With using same method like convert base 10 numbers to base 9 number, then gotten:
Numbers system base 4 (familiar with quaternary)
Number system base 4 is number system using 4 numbers, are:
0, 1, 2, and 3.
And its writng are 0₄, 1₄, 2₄, and 3₄
Formula for base 4 numbers:

Example:
- Convert numbers 2333₄ ke base 10 numbers
- Convert numbers 191 to base 4 numbers
  With using same method like convert base 10 numbers to base 9 number, then gotten:
Numbers system base 3 (familiar with ternery)
Number system base 3 is number system using 3 numbers, are:
0, 1, and 2.
And its writng are 0₃, 1₃, and 2₃. Formula for base 3 numbers:

Example:
- Convert numbers 1212₃ to base 10 numbers
- Convert numbers 50 to base 3 numbers
  With using same method like convert base 10 numbers to base 9 number, then gotten:
Numbers system base 2 (familiar with binary)
Number system base 2 is number system using 2 numbers, are:
0 and 1.
And its writng are 0₂ and 1₂
Formula for base 2 numbers:

Example:
- Convert numbers 10100₂ to base 10 numbers
- Convert numbers 20 to base 2 numbers
  With using same method like convert base 10 numbers to base 9 number, then gotten: