in the last presentation we completed introduction of various number systems in this lecture we will study binary number system a computer cannot operate on the decimal number they do their operation on binary logic so it is important to study binary number system and as we already know the base in case of binary number system is equal to 2 the base or radix R is equal to 2 in case of binary number system so we have 0 to 2 minus 1 digits because when the base is R we have 0 to R minus 1 distinct digits in the number system so 0 to 2 minus 1 is 0 and 1 so there are 2 digits in case of binary number system a 0 and a 1 the binary digits are also called as bits let me write this point binary digits they are 0 & 1 are called as bits so from now onwards I will use this word bit for 0 & 1 let us take one example of binary number the number is 1 0 1 0 1 this is the binary number and if you remember the last presentation we represented the quantity by a decimal number 7 3 9 2 and the weight of one's position is 10 raise to power 0 the weight of tens position is 10 raise to power 1 weight of this position is 10 raise to power 0 and weight of this position stand raise to power 3 this is what we saw in the last presentation and binary number is also weighted number decimal number is very number and binary number is also weighted number so there is a weight associated with each and every position in this case the weight of this position is 10 raise to power 0 because base in this case base in this case is equal to 10 but here base is equal to 2 so you can easily relate the weight of this position is 2 raised to power 0 in the same way weight of this position is 2 raised to power 1 2 raised to power 2 2 raised to power 3 and 2 raised to power 4 these are the weights for the position and we can write this number like this 1 multiplied by 2 raised to power 4 0 multiplied by 2 raised to power 3 1 multiplied by 2 raised to power 2 0 multiplied by 2 raised to power 1 and 1 multiplied by 2 days to power 0 we can definitely write this number like this and if we simplify this we will get the decimal equivalent of this number this number is in binary and if you want the decimal equivalent you have to simplify this you have to solve this so let's do it quickly 2 raised to power 4 is 16 so 1 multiplied by 16 0 multiplied by 8 1 multiplied by 4 0 x 2 and 1 x 1 1 multiplied by 16 is 16 0 x 8 is 0 1 multiplied by 4 is 4 0 x 2 is 0 and 1 into 1 is 1 and when you add this you will have 21 so the decimal equivalent of this binary number is 21 now you have clear idea about the weights of position in case of binary number but what if there is a binary point so let's take another example for this the number is 1 0 1 0 1 and there's a binary point this is not decimal point but binary point and after this binary point we have 1 1 now let's see how we can write this number in this form 1 multiplied by 2 raised to power 4 because the weight of this position is 2 raised to power 4 we have already seen I will just copy this down quickly 0 multiplied by 2 raised to power 3 now the weight of this position is 2 raised to power minus 1 because weight of this position is 2 raised to power 0 and before 0 we have minus 1 in the same way weight for this position is 2 raised to power minus 2 so we have to multiply 1 with 2 raised to power minus 1 plus let me slide the board 1 multiplied by 2 raised to power minus 2 so this is how we can represent this number with binary point now we will move to MSB and LSB MSB and LSB MSB is an abbreviation for most significant bit and LSB is an abbreviation for least significant bit we will try to understand MSB and LSB with the help of one example let's take a binary number one zero one zero one right and we have already seen this number is equivalent to twenty one in decimal the leftmost bit this leftmost bit is called is called MSB and this rightmost bit is called LSB now why this bit is called more significant bit and this bit is called least significant bit we have to see I will replace this one with zero one zero one zero zero I have replaced this bit with zero and the decimal equivalent of this number is equal to two 0:20 earlier it was 21 I replaced LSB I changed LSB from 1 to 0 and we have 2 0 20 not much difference but if I replace this one with 0 we will have 0 0 1 0 1 and the decimal equivalent of this binary number is 5 earlier we were having 21 but now we have 5 so the difference is 1 and difference in this case is 16 now what do you think out of these 5 bits which bit is most important and which at least let's name them the first bit is be zero second bit is B 1 B 2 B 3 and B 4 when we changed B 4 from 1 to 0 we have 5 the original number was 21 and the new number is 5 so there is a great difference between the original and new number on the other hand when we changed B 0 from 1 to 0 the new number is 20 an original number was 21 so the difference is not much hence we can say that the significance of leftmost bit is higher as compared to the significance of rightmost bit hence this bit is called I must be more significant bit and this bit is called LSB least significant bit this is all 4 MSB and LSB bit is a smallest unit of data bit is smallest unit of data and one nibble is equal to 4 bits and we use nibble to represent binary coded decimal BCD number and hexadecimal numbers because we require 4 bits to represent hexadecimal numbers on the other hand one byte is equal to 8 bits and one word is equal to 16 bits one double word double word is equal to 32 bits or we can say that one word is equal to 2 bytes and one double word is equal to 4 bytes this is all for this presentation see you in the next one