WEBVTT 00:00:01.000 --> 00:00:07.000 align:middle line:84% Now imagine once again that we have 8 cables and there's current on every cable 00:00:07.000 --> 00:00:11.000 align:middle line:84% so current on the first cable, second one and so forth and so on 00:00:11.000 --> 00:00:20.000 align:middle line:84% each cable has current, that means that this value is 128, 64, 32, and so forth 00:00:20.000 --> 00:00:22.000 align:middle line:84% If you add all those values together 00:00:22.000 --> 00:00:30.000 align:middle line:84% so 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1, you get a value of 255 00:00:30.000 --> 00:00:39.000 align:middle line:84% Thus 8 binary 1s equals 255 in decimal, that's because each logical cable 00:00:39.000 --> 00:00:43.000 align:middle line:84% is set on, in other words, it has a value of 1 and this value for example 00:00:43.000 --> 00:00:49.000 align:middle line:84% represents 2 to the power of 5 which equals 32 in decimal 00:00:49.000 --> 00:00:55.000 align:middle line:84% So adding all of those values together gives you a value of 255 in decimal 00:00:55.000 --> 00:00:59.000 align:middle line:84% So let's demonstrate this using a Windows calculator 00:00:59.000 --> 00:01:04.000 align:middle line:84% So in this example, I'm going to go to calculator and change it to programmer 00:01:04.000 --> 00:01:07.000 align:middle line:84% This allows me to see both decimal and binary values 00:01:07.000 --> 00:01:14.000 align:middle line:84% So 255 in decimal is equivalent to 8 binary 1s or once again 00:01:14.000 --> 00:01:18.000 align:middle line:84% 8 binary 1s is equivalent to 255 in decimal 00:01:18.000 --> 00:01:22.000 align:middle line:84% 255 in decimal is equivalent to 8 binary 1s 00:01:22.000 --> 00:01:29.000 align:middle line:84% So here's another example, what is the binary equivalent of 1 in decimal? 00:01:29.000 --> 00:01:35.000 align:middle line:84% So using our table, the decimal value is 1, that means that these values are 00:01:35.000 --> 00:01:39.000 align:middle line:84% are all turned off, in other words, the binary equivalent is 0 00:01:39.000 --> 00:01:43.000 align:middle line:84% for the first 7 values, but the last value is turned on 00:01:43.000 --> 00:01:50.000 align:middle line:84% So 1 in decimal is equivalent to 7 binary 0s followed by binary 1 00:01:50.000 --> 00:01:53.000 align:middle line:84% Once again using our Windows calculator 00:01:53.000 --> 00:01:56.000 align:middle line:84% 1 in decimal is equivalent to 1 in binary 00:01:56.000 --> 00:02:00.000 align:middle line:84% but because we're using this mainly with IP Addressing you'll tend to write 00:02:00.000 --> 00:02:05.000 align:middle line:84% it as follows, the Windows calculator removes the leading 0s 00:02:05.000 --> 00:02:10.000 align:middle line:84% So 1 in decimal is equivalent to 1 in binary, in this example what is 00:02:10.000 --> 00:02:14.000 align:middle line:84% equivalent binary value of 192 in decimal? 00:02:14.000 --> 00:02:21.000 align:middle line:84% So using our table 192 is equivalent to 128 + 64 which implies that the 00:02:21.000 --> 00:02:27.000 align:middle line:84% first bit is on and the second bit is on but the remaining bits are set to 0 00:02:27.000 --> 00:02:38.000 align:middle line:84% 128 + 64 = 192, thus, 11 followed by 6 binary 0s, is equivalent to 192 in decimal 00:02:38.000 --> 00:02:43.000 align:middle line:84% using our Windows calculator once again, a 192 in decimal equals 00:02:43.000 --> 00:02:52.000 align:middle line:84% 11000000 in binary which is once again the equivalent of 192 in decimal 00:02:52.000 --> 00:02:58.000 align:middle line:84% Here's another example, what is the binary equivalent of 253 in decimal? 00:02:58.000 --> 00:03:08.000 align:middle line:84% Now 253 in decimal is a 128 + 64 + 32 + 16 + 8 + 4 + 1 00:03:08.000 --> 00:03:11.000 align:middle line:84% and once again that gives you 253 00:03:11.000 --> 00:03:18.000 align:middle line:84% So 128 means the first or most significant bit is set on 00:03:18.000 --> 00:03:24.000 align:middle line:84% 64 implies the second bit is on, 32 means that the third bit is on 00:03:24.000 --> 00:03:29.000 align:middle line:84% 16 means the fourth bit is on, 8 means the fifth bit is on 00:03:29.000 --> 00:03:34.000 align:middle line:84% 4 means the sixth bit is on and the 1 means that the last bit 00:03:34.000 --> 00:03:40.000 align:middle line:84% or least significant bit is on, 2 is set off in this example 00:03:40.000 --> 00:03:46.000 align:middle line:84% So 253 in decimal is equal to 6 binary 1s followed 00:03:46.000 --> 00:03:50.000 align:middle line:84% by binary 0 followed by binary 1 00:03:50.000 --> 00:03:54.000 align:middle line:84% So 253 equals 6 binary 1s followed by 0, followed by 1 00:03:54.000 --> 00:03:59.000 align:middle line:84% So I am hoping at this point you have a good understanding on how to convert 00:03:59.000 --> 00:04:03.000 align:middle line:84% decimal to binary and back again. There are many tricks with regards to 00:04:03.000 --> 00:04:07.000 align:middle line:84% binary that can allow you to speed up the calculations 00:04:07.000 --> 00:04:15.000 align:middle line:84% One example would be that 255 - 2 = 253, in other words, this value is set off 00:04:15.000 --> 00:04:22.000 align:middle line:84% which allows you to work out that 255 looks like this but that bit is set off 00:04:22.000 --> 00:04:27.000 align:middle line:84% so 253 looks like this