Understanding Binary Codes and Their Applications
Binary coding is crucial for digital systems as they understand only 0s and 1s. This process converts information into binary language for processing by digital circuits. Different types of binary codes like weighted codes and BCD codes are used for error correction, digital communication, and computer applications. Packed BCD and valid BCD numbers are also part of this coding system, simplifying communication between man and machine.
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Presentation Transcript
coding The digital systems understands only 0 s and 1 s i.e. binary language Generally information is in numeric, alphabetic or alphanumeric form. Before processing the information by digital circuits information should be converted into binary language. Coding is a process of conversion of information into binary language.
Binary codes The codes in which the decimal digits 1 to 9 represented by binary digits is called binary codes Number of codes are developed to simplify the communication between machine and man. Generally information available in numerical, alphabetic or alphanumeric form and it will not be understood by digital circuits and digital systems so coding is needed.
Applications of codes Used for error correction and error detection in digital systems. Used in digital communication Used in digital computer
types Weighted code Non-weighted code
Weighted Code:- In weighted code, each digit position have a weight or value. The sum of all digits multiplied by a weight gives the total amount being represented. We can express any decimal number in tens, hundreds, thousands and so on. Eg:- Decimal number 4327 can be written as 4327= 4000+300+20+7 In the power of 10, it becomes 4327= 4(10 )+3(10 )+2(10 )+7(100) BCD or 8421 is a type of weighted code where each digit position is being assigned a specific weight.
BCD(binary coded decimal) or 8421 code:- It is composed of four bits representing the decimal digits 0 through 9. To represent any decimal number it uses 4 bit binary number. The 8421 indicates the binary weights of the four bits(2 ,2 ,2 ,20). Decimal 8421(BCD) 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001
Packed BCD The BCD numbers corresponding to decimal numbers beyond 9 are called as packed BCD Decimal (25) 0010 0101(Packed BCD)
Valid BCD Numbers Decimal 8421(BCD) 10 0001 0000 11 0001 0001 12 0001 0010 13 0001 0011 14 0001 0100 15 0001 0101 16 0001 0110 17 0001 0111 18 0001 1000 19 0001 1001 20 0010 0000 320 0011 0010 0000
Binary coded decimal 0010 0000= 8bits=1byte upper nibble lower nibble nibble= 4 bits
Applications of BCD Used in digital voltmeter, electronic calculator ,digital computers.
Solve the following Convert following to BCD form a) 47310 b) 31210 c) 25710 d) 11210 Convert following BCD to their decimal equivalent a) 10000110 b) 00110010.10010100 Convert the following binary number numbers to their BCD equivalent. a) 1101.012 b) 11.0112
BCD Addition Rules Add the given two bcd numbers If result is invalid bcd no. then add binary 6 into the result We get valid bcd result.
BCD addition 3 0011 8 1000 +4 0100 + 7 0111 ------ ------- 7 0111 15 1111 invalid bcd ------ --------- + 0110 --------- 1 0101 valid bcd 1 5
BCD Subtraction 4 0100 17 0001 0111 - 2 0010 - 8 0000 1000 borrow 1 ------------ ----------------------------- 0010 9 0000 1111 - 0110 ----------------------------- final answer 1001
BCD subtraction 555 0101 0101 0101 -234 0010 0011 0100 borrow 1 1 ------------------------------------------ 0011 0010 0001
BCD subtraction 898 1000 1001 1000 -259 0010 0101 1001 Borrow 11 1111 111 ----------------------------------------------- 649 0110 0011 1111 - ----------------------------------------------- 0110 0011 1001 0110
BCD Addition 17 00010111 58 01011000 --------------------------- 75 01101111 ------------------------ 0111 0101 0110
BCD Addition 569 0101 0110 1001 687 0110 1000 0111 ------------------------------ 1011 1111 0000 0110 0110 0110 ----------------------------------- 1 0010 0101 0110
Solve the following Perform BCD operation of 17+58 569+687 28+16 37+65 57+26 45+33 147+284 65-12 45-23 35-20
