How To Subtract Binary Numbers 15 Steps With Pictures

1 - 0 = 1 11 - 10 = 1 1011 - 10 = 1001

110 - 101 = ?

First, cross out the 1 and replace it with a 0, to get this: 1010 - 101 = ? You’ve subtracted 10 from the first number, so you can add this “borrowed” number to the ones place: 101100 - 101 = ?

101100 - 101 = ? The rightmost column is now: 10 - 1 = 1. If you can’t figure out how to reach this answer, here’s how to convert the problem back to decimal: 102 = (1 x 2) + (0 x 1) = 210. (The sub numbers indicate which base the number is written in. ) 12 = (1x1) = 110. Therefore, in decimal form this problem is 2 - 1 = ?, so the answer is 1.

101100 - 101 = __1 = _01 = 001 = 1.

10110000 - 111 = 10111001000 - 111 = (remember, 10 - 1 = 1) 10111001100100 - 111 = Here it is written more tidily: 1011100 - 111 = Solve column by column: _ _ _ _ 1 = _ _ _ 0 1 = _ _ 0 0 1 = _ 0 0 0 1 = 1 0 0 0 1

Add in binary to check your work. Add the answer together with the smaller number, and you should get the larger number. Using our last example (11000 - 111 = 10001), we get 10001 + 111 = 11000, which is the larger number we started with. Alternatively, convert each number from binary to decimal and see whether it is true. Using the same example (11000 - 111 = 10001), we can convert each number into decimal and get 24 - 7 = 17. This is a true statement, so our solution is correct.

We’ll use the example 101 - 11 = ?

101 - 011 = ?

What we’re actually doing is “taking the one’s complement,” or subtracting each digit in the term from one. The “switching” shortcut works in binary, since the only two possibilities result in switching the term: 1 - 0 = 1 and 1 - 1 = 0.

101 + 101 = 1010 If this does not make sense to you, review how to add binary numbers.

1010 = 10 Therefore, 101 - 011 = 10 If you don’t have an extra digit, you tried to subtract a larger number from a smaller one. See the tips section for how to solve problems like that, and start again.

56 - 17 Since we’re using base ten, we’ll take the “nine’s complement” of the second term (17) by subtracting each digit from nine. 99 - 17 = 82. Change this into an addition problem: 56 + 82. If you compare this to the original problem (56 - 17), you can see that we’ve added 99. 56+82=138. But since our changes added 99 to the original problem, we’ll need to subtract 99 from the answer. Again, we’ll use a shortcut, just like in the binary method above: add 1 to the total number, then delete the digit on the left (which represents 100): 138 + 1 = 139 → 139 → 39 This is finally the solution to our original problem, 56-17.