Find the value of 525₂ − 475₂
. (a) 100 (b) 10000 (c) 50000 (d) 100000

To find the value of \( 525_2 - 475_2 \), we first need to convert these binary numbers into decimal form.

Step 1: Convert Binary to Decimal

The binary number \( 525_2 \) can be broken down as follows:

• 5 in binary is \( 101 \) (which is \( 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5 \))
• 2 in binary is \( 10 \) (which is \( 1 \times 2^1 + 0 \times 2^0 = 2 + 0 = 2 \))

So, \( 525_2 = 5 \times 2^1 + 2 \times 2^0 = 10 + 2 = 12 \) in decimal.

Now for \( 475_2 \):

• 4 in binary is \( 100 \) (which is \( 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 = 4 + 0 + 0 = 4 \))
• 7 in binary is \( 111 \) (which is \( 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 4 + 2 + 1 = 7 \))

Thus, \( 475_2 = 4 \times 2^1 + 7 \times 2^0 = 8 + 7 = 15 \) in decimal.

Step 2: Perform the Subtraction

Now we can subtract the two decimal values:

\( 12 - 15 = -3 \).

Step 3: Convert Back to Binary

To express \(-3\) in binary, we typically represent it in two's complement. However, since the options provided are positive values, we can conclude that the subtraction yields a negative result, which is not listed among the options.

Final Answer

None of the provided options (a) 100, (b) 10000, (c) 50000, (d) 100000 are correct, as the result of \( 525_2 - 475_2 \) is \(-3\).