Numeral system

The Music Telegraph | Text 2019/01/23 [10:54]

Numeral system

The Music Telegraph| 입력 : 2019/01/23 [10:54]

 

 


 

Numeral system

 

 

 

Base 10: Decimal number

ex) 6357 = 6000 + 300 + 50 + 7

     = (10^3 x 6) + (10^2 x 3) + (10^1 x 5) + (10^0 x 7)

 

 

 

Base 2: Binary number

- Each digit is a bit (0, 1)

 

*1 Byte = 8 bits

 

1 Kilobyte (KB) = 2^10 bytes = 1024 bytes = 8192 bits

1 Megabyte (MB) = 2^20 bytes = 1,048,576 bytes

1 Gigabyte (GM) = 2^30 bytes

1 Terabyte (TB) = 2^40 bytes

1 Petabyte (PB) = 2^50 bytes

1 Exabyte (EB) = 2^60 bytes

1 Zetabyte (ZB) = 2^70 bytes

1 Yottabyte (YB) = 2^80 bytes

 

 

8 bits = 1 byte = 256 values (2^8)

 

ex) Table: decimal to binary (10101110)

  128 (2^7) 64 (2^6) 32 (2^5) 16 (2^4) 8 (2^3) 4 (2^2) 2 (2^1) 1 (2^0)
  1 0 1 0 1 1 1 0
200 1 1 0 0 1 1 0 1
212 1 1 0 1 1 0 1 1
150 1 0 0 1 0 1 1 0
94 0 1 0 1 1 1 1 0
80 0 1 0 1 0 0 0 0

 

 

 

 

Base 16: Hexadecimal

0 ~ 9 & A (=10), B (=11), C (=12), D (=13), E (=14), F (=15)

 

ex)

ABC2 = (16^3 x 10) + (16^2 x 11) + (16^1 x 12) + (16^0 x 2)

= 40960 + 2816 + 192 + 2 = 43970

 

A0B5 = (16^3 x 10) + (16^2 x 0) + (16^1 x 11) + (16^0 x 5)

= 40960 + 0 + 176 + 5 = 41140

 

 

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