Computer Lecture-2

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Numerical Systems
If x is a real positive number where:
x=(a_n a_(n-1)…a_0.b_1 b_2…)_10
Then the value of x is the summation of the two sequences:
?_(k=0)^n??a_k×?10?^k+?_(k=1)^???b_k ?10?^(-k) ??
If is a real positive binary number:
x=(a_n a_(n-1)…a_0.b_1 b_2…)_2
Then the value of x is the summation of the two sequences:
?_(k=0)^n??a_k×2^k+?_(k=1)^???b_k 2^(-k) ??
If is a real positive binary number:
x=(a_n a_(n-1)…a_0.b_1 b_2…)_16
Then the value of x is the summation of the two sequences:
?_(k=0)^n??a_k×?16?^k+?_(k=1)^???b_k ?16?^(-k) ??
Example: convert the decimal number (39.125) to binary hexadecimal and octal.
Solution:
We firstly convert the integer part of the real number as follows:
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