Binary-coded decimal, or BCD, stores each decimal digit separately in four bits. Excess-3 also encodes one decimal digit at a time, but adds three before converting that digit to binary. These are digit codes, not ordinary whole-number binary representations.
Worked example
Decimal 47 is BCD 0100 0111: one group for 4 and one for 7. In excess-3, add three to each digit, giving 7 and 10; the code becomes 0111 1010. Ordinary binary 47 would instead be 0010 1111.
What to watch for
BCD groups 1010 through 1111 are invalid decimal digits. A code converter must handle or explicitly exclude invalid input patterns.
Try it yourself
Encode decimal 25 in BCD and excess-3.
Answer: BCD is 0010 0101. Adding three to each digit gives 5 and 8, so excess-3 is 0101 1000.
How to study this topic
Treat a code as a mapping with an explicit convention. Write the input, encoded bits and decoded result side by side. For error-checking examples, distinguish detecting an error from locating and correcting it.
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Digital Electronics