BCD to decimal interpretation Given the BCD value 1000 0000 0011 (grouped as 4-bit BCD digits), what is the corresponding decimal number?
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
-
A8003
-
B803
-
C1003
-
D103
Answer
Correct Answer: 803
Explanation
Introduction / Context:Binary-Coded Decimal (BCD) represents each decimal digit separately using 4 bits. Correctly grouping the bits into nibbles is key to decoding.
Given Data / Assumptions:
- BCD bit string: 1000 0000 0011.
- Each nibble is a decimal digit 0–9.
- Most significant group is on the left.
Concept / Approach:Split into nibbles: 1000, 0000, 0011. Convert each nibble to decimal: 1000 → 8, 0000 → 0, 0011 → 3. Combine digits in order to form the decimal number 803.
Step-by-Step Solution:
1) Group the bit string into nibbles: 1000 | 0000 | 0011.2) Convert nibble-wise: 1000 → 8; 0000 → 0; 0011 → 3.3) Write digits sequentially: 8, 0, 3.4) Resulting decimal number = 803.Verification / Alternative check:Re-encode 803 into BCD: 8 → 1000, 0 → 0000, 3 → 0011, matching the given pattern.
Why Other Options Are Wrong:
- 8003/1003/103: Insert extra or missing digits not present in the 3-nibble BCD value.
Common Pitfalls:Failing to group into 4-bit chunks or interpreting as straight binary instead of BCD.
Final Answer:803