FINLANDIA SCHOOLA number system is a way of representing numbers.
The Base(or Radix) is the total number of unique digits used.
Base 10 (Decimal)
a) Digits: 0,1,2,3,4,5,6,7,8,9(10 total digits)
b) How it works: we use place values(units, tens, hundreds) based on power of 10.
e.g. 452=(4x10²) + (5x10¹) +(2x10°)=400+50+2
Base 2 (Binary)
Digits: 0,1 (2 total digits)
This is the native language of computers. A "1" is an "ON" electrical state; a "0" is an "OFF" state
Place values are based on powers of 2(1,2,4,8,16,32,64,128...)
e.g. 1011=(1x2³) + (0x2²) + (1x2¹) + (1x2°)=11
Base 16 (Hexadecimal)
Digits 0-9 and A,B,C,D,E,F(16 total digits)(A=10, B=11, C=12, D=13, E=14, F=15)
It is a human friendly shorthand for Binary. Long Binary strings are hard to read
Uses:
Memory address; e.g. 0x7FFF5BFFC60),
Web/CSS Colour codes: e.g. #FF0000=Red
Error messages.
Base 8(Octal)
Digits: 0,1,2,3,4,5,6,7(8total digits)
An older shorthand for binary (groups of 3 bits). Sometimes seen in file permissions on Linux/macOS.
Key conversion
1. Decimal to binary
method: repeatedly divide by 2 and record the remainders from bottom to top
e.g. 43
2. Binary to Decimal
method: use place value summation
3. Binary to Hexadecimal
method: group the binary strings into sets of four(from right to left)
4. Hexadecimal to Binary
method: convert each hex digits into its four-bit binary equivalent.