Math Is Fun Forum

user1234

Member

Registered: 2006-11-21

Posts: 8

this is mysterious! binary subtraction

hi. i have a problem with binary subtarction. i am trying to subtract 11010110 - 01000111 showing the difference and borrow as well but i get the wrong answer. can u help me?

                     1101 0110
                   -
                     0100 0111
-----------------------------------
Difference:        10010001
Borrow:         00000001(0)
-------------------------------------
Answer:           010010111

i get this as the answer but its not correct, because if you check this in Calculator (View > Scientific) you get the answer 10001111.
I cant see where i am going wrong. all help is greately appreciated!

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: this is mysterious! binary subtraction

1101 0110
         - 0100 0111
          ========
           1000 1111

You need to borrow for the first 5 (rightmost) columns.   Hopefully you can understand my notations.

             1                 
1101 0100              You must borrow for the first subtraction which makes the 1 in the 2's
0100 0111              column a 0
=======
              1

            1
1101 0000             You must borrow for the second subtraction also, making the 1 in the 4's
0100 0111             column a 0
=======
            11

          1
1100 1000             You must borrow again, this time from the 16's column.
0100 0111
=======
          111

1100 1000             Now it's easy with no more borrowing.
0100 0111
=======
1000 1111

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: this is mysterious! binary subtraction

I got 1000 1111, too, so this problem has been solved.

user1234

Member

Registered: 2006-11-21

Posts: 8

Re: this is mysterious! binary subtraction

thanks alot. that definately explained my problem!

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: this is mysterious! binary subtraction

Adding the inverse is typically much easier than subtraction.  However, if you've never heard of 2's complement, then you might as well stick to subtraction.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."