20 == 16 + 4
16 is 10000, 4 is 00100, so 20 must be 10100.
The above ideas lead to the repeated subtraction method of converting a reprsentation of a positive integer from decimal to binary.
Algorithm: Convert a positive integer from base 10 to Binary Representation |
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number = positive integer; while (number > 0 ) { determine the largest 2B that is less than or equal to number; put a 1 in the B's place of the binary ; number = number - 2B ; } Put 0s in the binary for the powers of 2 not used; |
You are (of course) eager to practice this method. Let us convert 23 to binary.
What is the greatest power of two less than 23?