# BCD Codes: Valid and Invalid Codes

## Understanding BCD Codes

**Binary Coded Decimal (BCD)** is a coding scheme used in digital systems to represent decimal numbers with binary codes. In BCD, each decimal digit is represented by a 4-bit binary code. For example, the decimal number 5 is represented as 0101 in BCD.

## Invalid BCD Codes

In BCD coding, the valid codes are those representing decimal numbers from 0 to 9 (binary 0000 to 1001). Any other combination of 4 bits that represent decimal numbers 10 to 15 are considered invalid BCD codes.

## Which of the following groups of codes represent all the invalid BCD codes?

a. 1001, 1010, 1011, 1100, 1101, 1110

b. 1010, 1011, 1100, 1101, 1110, 1111

c. 1000, 1001, 1010, 1011, 1100, 1110

d. 1000, 1001, 1010, 1011, 1100, 1101

Which of the following groups of codes represent all the invalid BCD codes? In BCD coding, the valid codes are those representing decimal numbers from 0 to 9 (binary 0000 to 1001). Thus, the invalid BCD codes are the ones representing decimal numbers 10 to 15 (binary 1010 to 1111), which corresponds to option b.