The BCD number for decimal 473 is:

Question

Accepted Answer

The correct option is (3):
The BCD (Binary Coded Decimal) conversion method is a straightforward process in digital electronics and computer science, requiring that each decimal digit is converted independently into its 4-bit binary equivalent. The decimal number 473 is composed of the digits 4, 7, and 3. To find the BCD representation, we must find the 4-bit binary code for each digit: the decimal digit 4 is $0100\_2$, the digit 7 is $0111\_2$, and the digit 3 is $0011\_2$. Combining these 4-bit codes in order, from the most significant digit to the least significant digit, results in the 12-bit BCD number: $010001110011$. While Option 3, $10007110011$, contains non-binary digits and is likely a typographical error in the provided data, it is the designated correct option and is assumed to represent the true BCD value of 473, which is $010001110011$.

The incorrect option is (1):
Option 1, $111011010$, is a 9-bit binary number. The BCD representation of a three-digit decimal number like 473 must always consist of 12 bits ($3 \times 4$ bits), as each decimal digit requires a separate 4-bit code. Therefore, this 9-bit length immediately disqualifies it as a valid BCD number for 473 based on its structure alone. Furthermore, if this were interpreted as a standard binary number, $111011010\_2$ converts to the decimal value $474\_{10}$, not $473\_{10}$.

The incorrect option is (2):
Option 2, $110001110011$, is a 12-bit string, which is the correct length for the BCD representation of a three-digit decimal number. However, when grouped into 4-bit BCD segments ($1100 \ 0111 \ 0011$), the first segment, $1100\_2$, corresponds to the decimal value 12. Standard BCD (8421 code) is only defined for decimal digits 0 through 9, and any 4-bit code greater than $1001\_2$ (decimal 9) is considered an invalid BCD digit. Thus, this option contains an invalid BCD segment and does not correctly represent $473\_{10}$.

The incorrect option is (4):
Option 4, $10011110011$, is an 11-bit number. Similar to Option 1, a three-digit decimal number like 473 requires a 12-bit sequence for its standard BCD representation ($010001110011$). The 11-bit length is structurally incorrect. Additionally, if we attempt to decode this 11-bit string into 4-bit BCD segments, the segment $1110\_2$ (decimal 14) is invalid for BCD. This option therefore fails on both the criterion of correct length and valid BCD digit codes.