Math Problem Statement

Based on the questions and answers from the provided image, identify the correct answers for BCD coding, binary conversions, and characteristics of different encoding schemes.

Solution

Let's analyze and solve each question from the image:

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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:

  1. How is Binary-Coded Decimal (BCD) used in digital systems?
  2. What are the differences between BCD and pure binary encoding?
  3. Why is Gray code preferred in some digital applications?
  4. How do you convert from decimal to Gray code?
  5. 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