Subtracting Binary Numbers

We want to subtract 1 from 10, both represented in base 2 (binary).

Step 1: Line Up the Numbers

First, we write down the two numbers so that they are aligned from the right. This makes it easier to subtract.

    10 (in base 2)
  -  1 (in base 2)
  

Step 2: Subtract the Rightmost Digits

We start by subtracting the rightmost digits (also known as bits in binary). In this case, that’s 0 from the first number and 1 from the second number.

Since 0 is smaller than 1, we need to borrow 1 from the next left digit (which is 1 in the first number).

Step 3: Perform the Borrow

After borrowing, the rightmost digit of the first number becomes 2 (in base 2, borrowing adds a ‘1’ to the rightmost digit and subtracts ‘1’ from the next left digit).

    10 (becomes 01 after borrowing)
  -  1
  -----
      1 (in base 2)
  

Final Result

The result of subtracting 1 from 10 in base 2 is 1 in base 2.