now given a binary sequence let us see how we can read it in terms of unsign sign and magnitude one's complement and two's complement assuming that you are given the following binary sequence 1 1 0 0 1 and a one so the weight of the first position is a 1 2 4 8 16 32 now I have been told that this binary sequence is in its unsigned form so in the unsigned notation what is the equivalent decimal number so unsigned is pretty easy take the take the weights and add it up so 32 + 16 + 2 + 1 which is equals to 48 + 250 51 so this binary sequence is 51 in unsigned notation I have given you a binary sequence in sign and magnitude form what is its equalent decimal number so let's take the number again now we know that in sign and magnitude the most significant bit is the sign if it is a one it indicates it's a negative number and if it's a zero it indicates it's a positive number and the magnitude will be this one which is basically 16 + 2 + 1 that is 19 so this number is 9 let's take the third variation which is now take the same binary sequence 1 1 0 0 1 1 now I have been told that the sequence is represented in its one's complement and you're asked to find out what does its equal equalent decimal number so the first thing that you want to do is check the sign since the sign bit is a one it's a negative number for sure now to find the equal and decimal number flip all the bits that's 0 0 1 1 0 0 which is equal to 12 so this number is -12 in one's complement finally you have the tw's complement so somebody has given me this binary sequence and they said that it's in two's complement and you're asked to find out its equalent decimal number again the process is very similar to your one's complement so check the sign bit since s bit is a one it's a negative number the next step is to flip all the bits and add one and this is equal to 13 so this binary sequence which is represented in two's complement is basically equivalent to -3 this is how you read sequences okay now given an unsigned 4bit number its range can go from 0 to 15 that is 2 4 - 1 in sign and magnitude it goes from - 7 to POS 7 in one's complement it goes from - 7 to 7 in two's complement it goes from - 8 to 7 and if you look at the generic formula so unsigned n bit will go from 0 to 2 to N - 1 sign and magnitude would be - 2 to n -1 + 1 to 2 to n -1 - 1 one's complement would be 2 to n -1 - 1 and finally you have the two's complement minus 2 to n [Music] -1 to 2 to n -1 -1