To solve the problem, we'll follow these steps:

1. Understand the binary representation:

   • The two binary numbers given are:
     • $\text{Binary 1: } 1111\ 1111\ 1111\ 1111\ 1111\ 1111\ 1111\ 1001$
     • $\text{Binary 2: } 0000\ 0000\ 0000\ 0000\ 0000\ 0000\ 0001\ 0101$
   • These are 32-bit binary numbers using two's complement representation.

2. Convert the binary numbers to decimal:

   • In two's complement, the most significant bit (MSB) determines the sign. If the MSB is 1, the number is negative; if it is 0, the number is positive.

   • For Binary 1:

     • MSB is 1, so the number is negative.
     • To find its decimal value:
       • Invert all bits and add 1 to the result.
       • Binary 1: $1111\ 1111\ 1111\ 1111\ 1111\ 1111\ 1111\ 1001$
       • Inverted: $0000\ 0000\ 0000\ 0000\ 0000\ 0000\ 0000\ 0110$
       • Add 1: $0000\ 0000\ 0000\ 0000\ 0000\ 0000\ 0000\ 0111$
       • Decimal value: $7$
       • So, Binary 1 is $-7$.

   • For Binary 2:

     • MSB is 0, so the number is positive.
     • Decimal value: $1 \times 2^4 + 1 \times 2^2 + 1 \times 2^0 = 16 + 4 + 1 = 21$
       • So, Binary 2 is $21$.

3. Subtract the binary numbers:

   • The problem asks to subtract Binary 2 from Binary 1: $-7 - 21 = -28$

4. Express the result in decimal:

   • The result of the subtraction is $-28$ in decimal.

So, the final answer is:

$\boxed{-28}$

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you convert a binary number to its two's complement?
2. How would you subtract two binary numbers directly without converting them to decimal first?
3. What is the significance of the most significant bit (MSB) in two's complement numbers?
4. How does the two's complement system differ from the sign-magnitude representation?
5. How would the operation change if the numbers were 16-bit instead of 32-bit?

Tip: When working with binary subtraction in two's complement, remember that subtraction can be done by adding the negative of the second number to the first.