i noticed some people have problems with the binary numbers in my avatar. let me help you:
1) the number in the second line, partially concealed by the Rat, is 10001.0001
2) the algorhytm of conversion from binary to decimal numbers is the following:
-above each binary digit, starting backwards, you must write the highest decimal number that could be displayed in a register in which that digit is the largest (assuming the first bit in the register is reserved for signum). not quite clear? ok, let's say you're converting the third digit, looking from backwards. the highest decimal value that can be displayed in register with n digits is 2^(n-1). in this case, n=3, so the highest value would be 2^(3-1) = 4. so, you must write 4 above the third digit. above the fourth digit, you must write 8, above the first you write 1, etc.
-if the digit contains 1, you must add the number written above to the final decimal number. if it contains 0, you mustn't add anything. here's a demonstration: let's convert number 1001101 to decimal.
64 32 16 8 4 2 1
1 - 0 - 0-1-1-0-1
digit 1 is below numbers 64, 8, 4 and 1, below other numbers is digit 0. that's why we must only add up numbers 64, 8, 4 and 1. so the final number would be 64 + 8 + 4 + 1 = 77. therefore, number 1001101, when converted into decimal system, is 77! simple as that!
converting the fractioned binaries is a bit more tricky. here's how you can do it. let's say you have a binary number 11.0101. every binary number can be displayed with binary exponent, where base is 2 instead of 10, as is with decimal numbers. for example, number 10.11 can be displayed as 0.1011 * 2^2, or as 1011 * 2^(-2), etc. back to our example - 11.0101 = 110101 * 2^(-4)
now you must convert 110101 into decimal, using the algorhytm explained above. 110101 = 53. now you have: 11.0101 = 110101 * 2^(-4) = 53 * 2^(-4) = 53 * 0.0625 = 3.3125 voila! conversion successful!
NOTE: converting the number 10001.0001 (you know, the one in my avatar) is a little tricky. you see, the 0001 part repeats infinitely! that's why if you convert this number, you won't get an accurate result - you will get a decimal number with four decimal digits. you must aproximate these 4 decimal digits with the first one. for example, if your result was 0.3475, the correct number would be 0.3. if it was 1.1893, the correct number would be 1.2, etc.
don't get discouraged by these "obstacles". keep trying, and good luck!
, then why doesn't anyone shut them down? the answer is simple: they don't care! so why should we?
