Prerequisite – Number System and base conversions
Excess-3 binary code is an unweighted self-complementary BCD code.
Self-Complementary property means that the 1’s complement of an excess-3 number is the excess-3 code of the 9’s complement of the corresponding decimal number. This property is useful since a decimal number can be nines’ complemented (for subtraction) as easily as a binary number can be ones’ complemented; just by inverting all bits.
For example, the excess-3 code for 3(0011) is 0110, and to find the excess-3 code of the complement of 3, we just need to find the 1’s complement of 0110 -> 1001, which is also the excess-3 code for the 9’s complement of 3 -> (9-3) = 6.
Converting BCD(8421) to Excess-3 –
As is clear by the name, a BCD digit can be converted to its corresponding Excess-3 code by simply adding 3 to it. Since we have only 10 digits(0 to 9) in decimal, we don’t care about the rest and marked them with a cross( X ).
Let
Let
The truth table for the conversion is given below. The X’s mark is don’t care condition.
To find the corresponding digital circuit, we will use the K-Map technique for each of the Excess-3 code bits as output with all of the bits of the BCD number as input.
Corresponding minimized Boolean expressions for Excess-3 code bits –
The corresponding digital circuit-
Converting Excess-3 to BCD(8421) –
Excess-3 code can be converted back to BCD in the same manner.
Let
Let
The truth table for the conversion is given below. The X’s mark is don’t care condition.
K-Map for D-
K-Map for C-
K-Map for B-
K-Map for A-
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Corresponding minimized boolean expressions for Excess-3 code bits –
The corresponding digital circuit –
Here