When we add 6 and 7 in BCD, we get 1101 which is an invalid state therefore, we add 0110 (6) to the sum to get correct result which is 0001 0011 (13). Example: Perform BCD Addition of 6 and 7 SolutionīCD representation of 6 is given as 0110 and for 7 it is 0111. The BCD addition, is thus carried out by individually adding the corresponding 4-bit groups starting from the LSB side and if there is a carry to the next group, or if the result belongs to any of the 6 illegal states than we add 6 10(0110) to the sum term of that group and resulting carry is added in the next group. Here, the rules of binary addition are partially applicable only to the individual 4-bit groups. The addition of BCD numbers is slightly different from binary addition. Binary Coded Decimal Addition (BCD Addition) Similarly, (53) 10 in BCD notation can be represented as (0101 0011). (28) 10 in BCD notation can be represented as (0010 1000). Decimal NumbersĮxample 1: Represent (28) 10 and (53) 10 in 8421 BCD notation Solution The following table describes the relation between Decimal, Binary and 8421 BCD numbers. Relation Between Decimal, Binary, and 8421 BCD Numbers Here, we require 8-bits to represent the same 13.Īnother disadvantage is that arithmetic operations become more complex as compared to the usual binary numbers because, in BCD numbers, we have 6 illegal states as 1010, 1011, 1100, 1101, 11 which are not part of 8421 BCD system. Usually, in binary numbers, we represent (13) 10 = (1101) 2 i.e., we require 4-bits but in BCD notation (13) 10 is represented as (0001 0011). Also, the sequential nature of BCD numbers makes it advantageous for performing arithmetic operations.Īlthough, there are many advantages there are some disadvantages too such as:īCD codes are more inefficient than usual binary codes. In a digital system that accepts only binary numbers in form of 0 and 1, the only way to interpret decimal numbers is its conversion from decimal to binary and vice-versa which is a slow process and it also requires a huge electronic circuitry. ![]() ![]() Since the weights are attached to it comes in the category of weighted codes and is also sequential. ![]() The 4-bit binary numbers have their weights attached as 8, 4, 2, 1 from MSB to LSB side. Prerequisite: Number systems Binary Coded Decimal (BCD Code)īCD Code (8421 Code): In BCD 8421 code, each decimal digit is represented using a 4-bit binary number. In this tutorial, we will learn about the binary-coded decimal (BCD code) and its addition (binary-coded decimal addition) with the help of examples.īy Saurabh Gupta Last updated : May 10, 2023
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