Converting Octal and Hexadecimal Constants to Decimal and Calculating Sum Using Twos-Complement Algorithm

1) What is the decimal-base value of the following octal/hex constants 042, 0X42, 0XFF, 0XCAB? 2) Write a C++ program that calculates the sum of the first two values above using the twos-complement algorithm.

Decimal Equivalents of the Octal and Hexadecimal Constants:

  • 042 (octal) = 34 (decimal)
  • 0X42 (hex) = 66 (decimal)
  • 0XFF (hex) = 255 (decimal)
  • 0XCAB (hex) = 32715 (decimal)

1) Converting Octal and Hexadecimal Constants to Decimal:

042 (octal) = 34 (decimal): To convert an octal number to decimal, we use the positional value of each digit in the octal number and multiply it by 8 raised to the power of its position. In this case, the octal number 042 has digits 4 and 2. The decimal equivalent is (4 * 8^1) + (2 * 8^0) = 32 + 2 = 34.

0X42 (hex) = 66 (decimal): To convert a hexadecimal number to decimal, we use the positional value of each digit in the hexadecimal number and multiply it by 16 raised to the power of its position. Here, the hexadecimal number 0X42 has digits 4 and 2. The decimal equivalent is (4 * 16^1) + (2 * 16^0) = 64 + 2 = 66.

0XFF (hex) = 255 (decimal): The "O" in front of the hexadecimal number indicates that it is in octal format. However, it seems to be a typo, and we can safely ignore it. So, the hexadecimal number 0XFF has digits F and F, which represent 15 each in decimal. The decimal equivalent is (15 * 16^1) + (15 * 16^0) = 240 + 15 = 255.

0XCAB (hex) = 32715 (decimal): Similarly, the "O" in front of the hexadecimal number indicates that it is in octal format, but it's likely another typo. The hexadecimal number is actually 0XCAB, with digits C, A, and B. Converting each digit to decimal, we get (12 * 16^2) + (10 * 16^1) + (11 * 16^0) = 3072 + 160 + 11 = 32715.

2) C++ Program to Calculate the Sum Using Twos-Complement Algorithm:

To calculate the sum of the first two values (34 and 66) using the twos-complement algorithm in C++, you can create a function like this:

int sum(int x, int y) {
    int sum = x + y;
    return sum;
}

By calling this function with the values 34 and 66, you will get the sum of 100, which is the correct result based on the conversions of the octal and hexadecimal constants to decimal.

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