Suppose a binary number 11002 and we will convert it into decimal form. The binary number has base 2. In the number (1100)2 , 0 is the least significant digit and 1 is most significant digit. We will multiply each digit with the base 2 to the power index number. So binary number (1100)2 has following index number of each digit-
3 2 1 0 ---- index number or order of digit. It starts from 01 1 0 0 ---- the number
So, the multiplication will be like:
1100 = 1×23 + 1×22 + 0×21 + 0 × 20 = 8 + 4 + 0 + 0 = 12
So, the decimal value of binary number (1100)2 is (12)10
The fraction number can also be done in similar way but that time the power will be negative. Suppose the number (0.011)2 .
0.011 = 0×2-1 + 1×2-2 + 1×2-3 = 0 + .25 + .125 = 0.375
So, the decimal value of binary number (0.011)2 is (0.375)10
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