A computer uses 32-bit as a Word for storing data and instruction. In terms of  the 2's complement binary number system, what is the result of conducting the arithmetic for the following two binary numbers (the result is to be expressed in decimal number):
0000 0000 0000 0000 0000 0000 0011  1101
plus
1111 1111 1100 1010 1111 0001  0001  0111
Please note that there is no space in the computer memory for storing the binary numbers; a space is included here for the "convenience of our human eyes".

To solve the problem of adding two 32-bit binary numbers in a 2's complement system and expressing the result in decimal, we can follow these steps:

1. **Interpret the Binary Numbers**: Identify whether each binary number is positive or negative based on the most significant bit (MSB).
   - If the MSB (leftmost bit) is `0`, the number is positive.
   - If the MSB is `1`, the number is negative.

2. **Convert the Binary Numbers to Decimal**: Convert both numbers to their decimal equivalents.

3. **Add the Two Numbers**: Perform the arithmetic addition.

4. **Express the Result**: Convert the final binary sum into its decimal equivalent.

### Step 1: Interpret the Binary Numbers
Given binary numbers:
- First number: `0000 0000 0000 0000 0000 0000 0011 1101`
- Second number: `1111 1111 1100 1010 1111 0001 0001 0111`

- The first number has MSB `0`, so it's positive.
- The second number has MSB `1`, so it's negative.

### Step 2: Convert the Binary Numbers to Decimal

#### First Number (Positive):
The binary `0000 0000 0000 0000 0000 0000 0011 1101` in decimal:
- Directly convert it as a positive binary number.

\[ 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 = 61 \]

#### Second Number (Negative):
The binary `1111 1111 1100 1010 1111 0001 0001 0117` is in 2's complement form.

To find its decimal equivalent:
1. Invert the bits: `0000 0000 0011 0101 0000 1110 1110 1000`.
2. Add 1 to the inverted bits to get the positive version:
   - `0000 0000 0011 0101 0000 1110 1110 1001`
3. Convert the result to decimal:
   - This equals 14,472,441
   - Then, negate the result to represent the original negative number:
   - Decimal Value = \[-14,472,441]

### Step 3: Add the Two Numbers
Now add the decimal equivalents:

\[ 61 + (-14,472,441) = -14,472,380 \]

### Step 4: Result
The final result in decimal is \(-14,472,380\).

Do you want further clarification or details?

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Here are some follow-up questions:
1. How does the 2's complement system work with signed integers?
2. How do you convert a negative 2's complement binary number to decimal?
3. What happens if the sum of two 32-bit numbers exceeds the 32-bit range?
4. What is the role of the most significant bit (MSB) in 2's complement?
5. How can you detect overflow in binary arithmetic?

**Tip**: Understanding how to convert 2's complement binary to decimal will help in interpreting both positive and negative binary numbers correctly.

Learn how to add two 32-bit binary numbers in the 2's complement system and convert the result to decimal. This problem involves understanding binary arithmetic, 2's complement representation, and converting binary to decimal. Suitable for advanced high school students and above.

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