BCD to Excess3 conversionTo understand the process of converting BCD to Excess3, it is required to have knowledge of Number System and Number Base Conversion. The Excess3 binary code is an example of a selfcomplementary BCD code. A selfcomplementary binary code is a code which is always complimented in itself. By replacing the bit 0 to 1 and 1 to 0 of a number, we find the 1's complement of the number. The sum of the 1'st complement and the binary number of a decimal is equal to the binary number of decimal 9. The process of converting BCD to Excess3 is quite simple from other conversions. The Excess3 code can be calculated by adding 3, i.e., 0011 to each fourdigit BCD code. Below is the truth table for the conversion of BCD to Excess3 code. In the below table, the variables A, B, C, and D represent the bits of the binary numbers. The variable 'D' represents the LSB, and the variable 'A' represents the MSB. In the same way, the variables w, x, y, and z represent the bits of the Excess3 code. The variable 'z' represents the LSB, and the variable 'w' represents the MSB. The 'don't care conditions' is expressed by the variable 'X'.
Now, we will use the Kmap method to design the logical circuit for the conversion of BCD to Excess3 code as: So, w=A+BC+BD Example: (100001011001)_{BCD} To find the Excess3 code of the given Excess3 code, first, we will make the group of 4 bits from right to left. Then, we will add 0011 in each group of 4 bits in order to get the excess3 code. Excess3 to BCD conversionThe process of converting Excess3 to BCD is opposite to the process of converting BCD to Excess3. The BCD code can be calculated by subtracting 3, i.e., 0011 from each fourdigit Excess3 code. Below is the truth table for the conversion of Excess3 code to BCD. In the below table, the variables w, x, y, and z represent the bits of the Excess3 code. The variable 'z' represents the LSB, and the variable 'w' represents the MSB. In the same way, the variables A, B, C, and D represent the bits of the binary numbers. The variable 'D' represents the LSB, and the variable 'A' represents the MSB. The 'don't care conditions' is defined by the variable 'X'.
Now, we will use the Kmap method to design the logical circuit for the conversion of Excess3 code to BCD as: So, w=AB+ACD Example: (101110001100)_{Excess3} To find the BCD code of the given BCD number, first, we make the group of 4 bits from right to left. Then, we subtract 0011 in each group of 4 bits in order to get the BCD code.
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