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Question

The Complementary Coded Decimal (CCD) code for decimal 325 is:

The correct answer is

1100 1101 1010

This question asks for the Complementary Coded Decimal (CCD) code for the decimal number 325. While "CCD" isn't a standard term, analysing the options and the provided correct answer suggests it refers to the bitwise inversion of the standard Binary Coded Decimal (BCD) representation for each digit.

Understanding BCD Conversion

First, let's recall the standard Binary Coded Decimal (BCD) representation. In BCD, each decimal digit (0-9) is represented by its unique 4-bit binary equivalent.

  • Decimal digit 3 is represented as $0011$ in BCD.
  • Decimal digit 2 is represented as $0010$ in BCD.
  • Decimal digit 5 is represented as $0101$ in BCD.

Therefore, the standard BCD code for the decimal number 325 is $0011\ 0010\ 0101$.

Calculating the CCD Code for 325

Based on the options, the Complementary Coded Decimal (CCD) code appears to be derived by taking the 4-bit BCD code for each decimal digit and inverting each bit (0 becomes 1, and 1 becomes 0).

Let's apply this process to each digit of 325:

  1. Digit 3:
    • BCD representation: $0011$
    • Inverting each bit: $1100$
  2. Digit 2:
    • BCD representation: $0010$
    • Inverting each bit: $1101$
  3. Digit 5:
    • BCD representation: $0101$
    • Inverting each bit: $1010$

Combining these inverted BCD codes gives the CCD code for 325:

$1100\ 1101\ 1010$

Matching with Options

Now, let's compare this result with the given options:

Option 1 $1100\ 1010\ 1101$
Option 2 $1101\ 1010\ 1100$
Option 3 $1100\ 1101\ 1010$
Option 4 $1111\ 1010\ 1101$

Our calculated CCD code, $1100\ 1101\ 1010$, matches Option 3.

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Important Questions from Number System and Binary Codes

  1. The binary equivalent of the decimal number 10 is __________.

  2. The decimal number 76 in hexadecimal and BCD number system is respectively;

  3. The binary equivalent of the decimal number 10 is __________.

  4. The steps for subtracting two positive numbers (M−N) using (r−1)'s complement are:

    (A) Add the minuend M to the (r−1)'s complement of the substrahend N.

    (B) If an end carry occurs, add 1 to the least significant bit.

    (C) If end carry does not occur, take the (r−1)'s complement of the number obtained in step A and place negative sign in front

    (D) Take (r−1)'s complement of the number obtained in step B on step C.

    Choose the correct answer from the options given below:

  5. A number may be represented in various number systems. Arrange the following number systems in ascending order based on the number of bits needed to represent the same number.

    A. Binary

    B. Decimal

    C. Hexadecimal

    D. Octal

    Choose the correct answer from the options given below

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