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I am studying Computational Mathematics, more specifically Numbering Systems and their conversion.
Numbering Systems are widely used in programming and computing in general, so my study focused more specifically on the 4 essential types used in computing:
- Sistema decimal N = {0,1,2,3,4,5,6,7,8,9}
- Binary system N = {0,1}
- Octal system N = {0,1,2,3,4,5,6,7}
- Sistema hexadecimal N = {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}
My doubt is limited to how to make the base conversion faster and more effective?
There is a method or methodology to perform the base conversion faster and more effectively?
Knowing that to convert a number from one base to another is necessary a large calculation and specific rules.
Conversão de Hexadecimal para Decimal
A regra é a mesma da conversão de qualquer sistema de numeração para o decimal.
AFC0,7D = ?
Ax16³ + Fx16² + Cx16¹ + 0x16° + 7x16-¹ + Dx16-²
10x16³ + 15x16² + 12x16¹ + 0x16° + 7x16-¹ + 13x16-²
44992,4882810
Note above that the hexadecimal system shown above is positional starting from right to left, so the base is raised to (16¹, 16°,16-¹) and also note that each digit has been multiplied by 16 because the hexadecimal numbering system is composed of base equal to 16. So 16 distinct digits.
I think only by understanding each system itself, then the conversion becomes more fluid. Understanding the formula is simpler than memorizing it.
– Jéf Bueno