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QuestionCalculate 110012−1111211001_{2} - 1111_{2}. What is the result?

Studdy Solution

STEP 1

Assumptions1. The numbers given are in binary format (base). . We need to perform the subtraction operation on these binary numbers.

STEP 2

To subtract binary numbers, align them such that the least significant bits are on the same column. Write the first number above the second number.
11001−1111\begin{array}{cccccc} &1 &1 &0 &0 &1 \\ - & &1 &1 &1 &1 \\ \end{array}

STEP 3

Start from the rightmost column and perform the subtraction. If the top bit is smaller than the bottom bit, borrow1 from the next left column.
In the rightmost column,1 -1 =0.
11001−11110\begin{array}{cccccc} &1 &1 &0 &0 &1 \\ - & &1 &1 &1 &1 \\ \hline & & & & &0 \\ \end{array}

STEP 4

In the second column from the right,0 -1. Since0 is smaller than1, we need to borrow1 from the next left column.After borrowing, the second column from the right becomes10 -1 =1 and the third column from the right becomes0 -1.
101001−111110\begin{array}{cccccc} &1 &0 &10 &0 &1 \\ - & &1 &1 &1 &1 \\ \hline & & &1 & &0 \\ \end{array}

STEP 5

In the third column from the right, we have0 -1. Again, we need to borrow1 from the next left column.
After borrowing, the third column from the right becomes10 -1 =1 and the fourth column from the right becomes0 -1.
0101001−1111110\begin{array}{cccccc} &0 &10 &10 &0 &1 \\ - & &1 &1 &1 &1 \\ \hline & &1 &1 & &0 \\ \end{array}

STEP 6

In the fourth column from the right, we have0 -1. Again, we need to borrow1 from the next left column.
After borrowing, the fourth column from the right becomes10 -1 =1 and the fifth column from the right becomes0 -1.
10101001−11111110\begin{array}{cccccc} &10 &10 &10 &0 &1 \\ - & &1 &1 &1 &1 \\ \hline &1 &1 &1 & &0 \\ \end{array}

STEP 7

In the leftmost column, we have10 -1 =1.
10101001−111111110\begin{array}{cccccc} &10 &10 &10 &0 &1 \\ - & &1 &1 &1 &1 \\ \hline &1 &1 &1 &1 &0 \\ \end{array} So, 110012−11112=11110211001_{2}-1111_{2}=11110_{2}.

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