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Decimal Equivalent of Largest Unsigned Binary: 8bits=256, n bits
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[QUOTE="Magna Visus, post: 4512138, member: 488295"] Hope this can be some sort of a tool to help you: Suppose your have a decimal number X and you want to convert it into the binairy number N made of n bits. 1st of all, in a general fashion: X=[itex]a_{0}[/itex]*[itex]2^{0}[/itex]+[itex]a_{1}[/itex]*[itex]2^{1}[/itex]+[itex]a_{2}[/itex]*[itex]2^{2}[/itex]...[itex]a_{n-1}[/itex]*[itex]2^{n-1}[/itex] If n=8, the highest number will be 255, and in binairy it is written as 11111111. Keep in mind that each "number 1" is the value of a specific [itex]a_{i}[/itex] And the reading directions of these values are opposite i.e. [itex]a_{0}[/itex] is the first "1" from the right of 11111111, [itex]a_{1}[/itex] is the 2nd one. For example: 11001001 [itex]a_{0}[/itex] =1 [itex]a_{1}[/itex] =0 [itex]a_{2}[/itex] =0 . . . [itex]a_{7}[/itex] =1 2nd of all: How did I transform 255 to the number 11111111? Here's a general method (Bear in mind there are other methods): Take your n bit number (let's consider 186 to add diversity, and in this case it's 8 bits): Is 186 >= [itex]2^{7}[/itex]=128? Yes. thus: [itex]a_{7}[/itex]=1. Now take 186 and substract [itex]2^{7}[/itex] => 58. And redo the operation: Is 58 >= [itex]2^{6}[/itex]=64? No. thus: [itex]a_{6}[/itex]=0. Do not substract anything since 58<64 Now go to the 3rd digit. Is 58 >= [itex]2^{5}[/itex]=32? Yes. thus [itex]a_{5}[/itex]=1. 58-32=26. Is 26 >= [itex]2^{4}[/itex]=16? Yes. thus [itex]a_{4}[/itex]=1. Is 26-16=10 > [itex]2^{3}[/itex]=8? Yes. thus [itex]a_{3}[/itex]=1. Is 10-8 >= [itex]2^{2}[/itex]=4? No. thus [itex]a_{2}[/itex]=0. Is 10-8>= [itex]2^{1}[/itex]=2? Yes. thus [itex]a_{2}[/itex]=1. Is 2-2 >= [itex]2^{0}[/itex]=1? No. thus the last digit on the right is 0. Result: 10111010 Verification: 128+0+32+16+8+0+2+0=186. The operation is correct. Hope this helps and clearify the idea of binairy to decimal transformation and vice-versa . [/QUOTE]
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Decimal Equivalent of Largest Unsigned Binary: 8bits=256, n bits
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