BCD to Gray code converter

The truth table having the conversion from BCD code to gray code is shown below. Since the BCD code has only 4 bits, a total of 9 BCD digits have been considered. The output is unpredictable for other input combinations.

From the minterms of each output G3, G2, G1, G0, the karnaugh map is implemented to simplify the function.

The code converter circuit for BCD to gray code is drawn as below from the obtained expression.

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Gray code to Excess-3 code converter

For this conversion, 4-bit gray code is considered as an input, which produces 4-bit excess-3 code as the output. Since 4-bit is considered for excess-3 code, the maximum possible output will be ‘1111’. Hence up to 12 numbers are considered for this conversion.

The truth table for this conversion is shown below. For understanding purposes, the decimal number and binary code are included in the below table.

The minterms of each output E3, E2, E1, E0 are plotted in the karnaugh map and is simplified as below.

In the k-map shown above for E0 output, although 2 to 3 pairs of cells can be grouped, all the minterms are marked as isolated cells to make simplification easier.

Here you can see the actual boolean expression obtained from the K-map for E0 output and you can also see, how it is simplified to get the minimal expression.

From the obtained expression for E3, E2, E1, E0, the code converter circuit for gray to excess-3 is drawn as below.