Explore the basics of Binary-Coded Decimal (BCD) representation with this quiz designed to deepen your understanding of BCD encoding, conversion, and key concepts. Ideal for learners seeking clarity on decimal-to-binary encoding and related digital systems terminology.
Which of the following correctly shows the BCD representation of the decimal number 7?
Explanation: The correct BCD representation for decimal 7 is 0111, as each decimal digit is encoded with its 4-bit binary equivalent. 0007 is not a proper binary format. 1110 is the binary for decimal 14, not 7, while 1010 is the binary for decimal 10 and is not a valid BCD digit. Only 0111 accurately represents 7 in BCD.
What is the valid range of individual digits that can be represented in standard BCD?
Explanation: Standard BCD assigns a unique 4-bit code to each decimal digit from 0 to 9. While 0 to 15 fits in 4 binary bits, BCD does not use codes for 10 to 15. The range 1 to 10 skips 0 and incorrectly includes 10; 0 to 7 only accounts for three bits, not four.
How is the decimal number 25 represented in BCD?
Explanation: In BCD, each decimal digit is encoded separately, so '2' becomes 0010 and '5' becomes 0101, resulting in 0010 0101. 11001 is pure binary, not BCD. 1010 0101 uses an invalid BCD digit (1010) and 1001 0100 represents the digits 9 and 4, not 2 and 5.
In standard (8421) BCD, how does the encoding of decimal 13 differ from its regular binary representation?
Explanation: BCD encodes each digit separately, so 13 becomes 0001 (for '1') and 0011 (for '3'), written as 0001 0011. The pure binary for 13 is 1101. Other options mix up the encoding or use invalid patterns for either BCD or binary.
Why is BCD often preferred over straight binary in digital displays such as calculators?
Explanation: BCD simplifies converting binary signals directly into decimal digits, which is useful for displays. It does not always use fewer bits—BCD is often less space-efficient. Arithmetic operations are not inherently faster, and BCD with four bits covers 0 to 9, not up to 15.
Which of the following is not a valid single-digit BCD code?
Explanation: In BCD, valid codes range from 0000 (0) to 1001 (9). 1011 represents decimal 11, which is not a legal BCD digit. 1001 is the code for 9, 0100 for 4, and 0001 for 1, all valid single-digit BCD codes.
Is the 4-bit code 1100 a valid BCD representation for any decimal digit?
Explanation: BCD uses only the codes 0000 to 1001 for single decimal digits. 1100 is the binary for 12 and is not valid in standard BCD. BCD does not use codes for two-digit numbers in a single block, nor is it intended for hexadecimal digits in its standard form.
How is the decimal number 05 represented in 8-bit BCD format?
Explanation: Each decimal digit gets its own 4-bit code, so '0' is 0000 and '5' is 0101. Thus, '05' is 0000 0101. 101 0000 swaps the positions and is not a valid BCD format. 0101 0000 would mean '50', and 1000 0101 is not correct for '05'.
What is the decimal value of the BCD code 0011 1000?
Explanation: Split the code into two 4-bit parts: 0011 is 3 and 1000 is 8, so the decimal number is 38. The number 24 would require codes for 2 and 4, not 3 and 8. 17 represents different BCD digits, and 81 reverses the digit order.
When adding two BCD digits, what is done if the result exceeds 9 (1001 in binary)?
Explanation: The rule in BCD arithmetic is to add 6 (0110 in binary) when the sum of digits exceeds 9, to adjust the result back into the valid BCD range. Subtracting 2 or converting to hexadecimal does not provide a valid BCD digit. Ignoring the carryover results in an invalid value.