Math Problem Statement
Solution
Let's analyze and solve each question from the image:
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Question 1: The question asks for the BCD (Binary-Coded Decimal) equivalent of the decimal number 473.
- In BCD, each decimal digit is represented by its binary equivalent.
- 4 in decimal is 0100 in BCD.
- 7 in decimal is 0111 in BCD.
- 3 in decimal is 0011 in BCD.
- Therefore, 473 in BCD is 0100 0111 0011.
- The correct answer is (b) 110001110011.
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Question 2: The question asks which option is not a valid BCD code.
- Valid BCD codes only represent decimal digits (0 to 9) using binary.
- Option (d) 1010 represents a binary value of 10, which is invalid in BCD.
- The correct answer is (d) 1010.
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Question 3: The question asks for the decimal equivalent of the BCD code
1001 0000 0101
.- Splitting the BCD code:
1001
(9),0000
(0),0101
(5). - This represents the decimal number 905.
- The correct answer is (a) 905.
- Splitting the BCD code:
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Question 4: This question is about the characteristics of BCD coding.
- The correct statement about BCD is that it only represents the digits 0 to 9.
- The answer is (d) Only the BCD codes for digits 0–F are valid.
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Question 5: This question asks about the main characteristic of a code where only one bit changes between each consecutive code.
- This characteristic is specific to Gray code.
- The correct answer is (d) Gray.
Do you need further details or have any questions about these explanations?
Here are five additional related questions to explore:
- How is Binary-Coded Decimal (BCD) used in digital systems?
- What are the differences between BCD and pure binary encoding?
- Why is Gray code preferred in some digital applications?
- How do you convert from decimal to Gray code?
- What are some advantages of using ASCII over BCD in modern computing?
Tip: When working with BCD, remember that it is limited to representing decimal digits, which is why each group of four bits in BCD must be between 0000 and 1001.
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Math Problem Analysis
Mathematical Concepts
Binary-Coded Decimal (BCD)
Binary Number System
Gray Code
ASCII
Formulas
BCD conversion from decimal
Binary-to-decimal conversion
Theorems
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Suitable Grade Level
Grades 10-12