### Example of decimal to binary conversion:

The decimal positive integer 330 can be deconstructed:

330

_{10}= 3*100 + 3*10 + 0*1 = 1*10

^{2}+ 2*10

^{1}+ 5*1

^{0}.

Each digit to the left has a multiplier that is 10 times the previous digit. Binary representations of positive integers can be understood in a similar way as their decimal counterparts. For instance:

99

_{10}= 1*64 + 1*32 + 0*16 + 0*8 + 0*4 + 1*2 + 1*1 = 1*2

^{6}+ 1*2

^{5}+ 0*2

^{4}+ 0*2

^{3}+ 0*2

^{2}+ 1*2

^{1}+ 1*2

^{0}.

or 99

_{10}= 1100011

_{2}

The subscript 2 denotes a binary number and the subscript 10 denotes a decimal number. The number 1100011

_{2}is represented by 7 bits. Any number can be converted from decimal to binary, by finding all of the powers of 2 that add up to the number in question. In our case the powers were 2

^{6}, 2

^{5}, 2

^{1}and 2

^{0}. You can see this is similar to the decimal deconstruction of the number 330 that was done earlier.

Signed Binary Converter