 Welcome everyone. My name is Ms. Shweta S. Patil working as an assistant professor in electronics and telecommunication engineering department at Varchan Institute of Technology, SolarPool. Today we are going to discuss the course in binary number system. Learning outcomes. At the end of the session, the learners will be able to explain commonly used binary codes. Explain gray code. Contents. First is the binary number system. Second is the weighted binary number system. Third is the definition of code and binary code. Fourth is the classification of binary code. Fifth is the explanation of weighted binary code and sixth is the explanation of gray code. Binary number system. Base or radix represented as r of the number system. The base or radix of number system is defined as the number of different symbols that is digits or characters used in that system. Here four types of number system is shown. For the decimal number system base is 10, so symbols used in that are 0 to 9. In binary number system base is 2 because 0 and 1 two symbols are used. In octal number system 8 is the base because symbols used from 0 to 7. In hexadecimal number system base is 16 because 0 to 9 digits are used and a to f characters are used in that number system. This is the one of the example for the binary number system. From bit 7 to bit 0 here 0 1 0 1 0 1 0 1 binary number is represented. Here total 8 bits are there from 0 to 7. Bit 0 is called as least significant bit that is LSB. Bit 7 is called as most significant bit that is MSB. Group of four bit is known as one nibble. Group of eight bits is always known as one byte. Group of 16 bits is always known as one word or it may be called as two bytes. Weighted binary number system the weight of digit of the binary number system is 2. Whenever any binary number appears its decimal equivalent can be found easily as follows. When there is a one in digit position weight of that position should be added. When there is a zero in digit position weight of that position should be disregarded. For example in this binary number 1 1 0 0 it has decimal equivalent 12 because for this one we are taking 8 and for this one we are taking 4 and others 2 there is a zero existing so weight of that position is disregarded and after adding we get the 12 as a decimal number here definition of code and binary code. The digital data is represented stored and transmitted as group of binary bits so this group is also called as binary code. When there is a binary code there should be 0 and 1 classification of binary codes the codes are broadly categorized into the following four categories first is the weighted code second is the non-mated code third is the alphanumeric code and fourth is the error detecting and correcting code weighted binary codes weighted binary codes are those binary codes which obey the positional weight principle. Each position of the number represents a specific weight for example the codes 8 4 2 1 bcd code 2 4 2 1 bcd code 5 2 1 1 bcd code are all weighted codes because code or 8 4 2 1 code which is the commonly used code. The full form of bcd is the binary coded decimal since this is coding scheme relating decimal and binary numbers four bits are required to code each decimal number for example 35 to the base 10 is represented as this because here for the three decimal number we are representing binary number at 0011 8 4 2 1 2 plus 1 will give 3 and for 5 if 0 1 0 1 is there then neglecting this 2 0 we are thinking about this 1 and 1 8 4 2 1 so 4 plus 1 will give the 5 35 to the base 10 is represented as this in binary binary and bcd code binary is the number system bcd is the code so both representation in the binary number system is different from the example it is clear that it requires more number of bits to code a decimal number using bcd code than using the straight binary code however in spite of this it is convenient to use bcd code for input and output operations in digital system here example is given give the binary and bcd equivalent for the decimal number 12 solution of that binary equivalent of decimal number 12 is 1 1 0 0 and bcd equivalent for decimal number is 8 bits here for 1 3 times 0 and 1 and for 2 0 0 1 0 give the bcd equivalent for decimal number 589 solution the decimal number is 589 so for that bcd code is represented like this for each decimal number there are four bits binary and gray codes the gray code may contain any number of bits gray code is always represented as n plus 1 gray code here we take the example of four-bit gray code it is compared with the four-bit binary code here here the from 0 to 7 msb all are 0 and from 8 to 15 msb is the 1 here and last three bits are 000 for the 0th combination for the last combination same 000 both are same and for the second combination and this 14th combination 0001 and 0001 both are same so from here if you are observing these last three bits are reflected these 0 and these 0 are same same if we are observing here 0001 and here also 0001 so we can conclude from that that is the property of gray code and we conclude that the gray code is the code where one bit will be deferred to the preceding number for example decimal number 13 and 14 are represented by gray code numbers 1011 and 101 these number differ only in single bit position here this bit one is different here bit one is one and in this bit one is zero so differ in only one single position gray code is a reflected code application of that is to maintain adjacency property gray code sequence is used in the k-maps because any two adjacent cells will differ by only one bit these are the references thank you