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### Binary Subtraction

```
Date: 03/25/2002 at 01:03:54
From: Robert
Subject: Binary Subtraction

I have checked the examples given on binary subtraction, but I keep
getting lost when doing the following:

1011000 - 110010

I know from the 2^0 column that 0-0 = 0. Then in the 2^1 column I need
to borrow, but I can't borrow from the 2^2 column, so I borrow from
the 2^3 column, which messes everything up. Can I be guided through
this example? I think it involves a 'next power' borrow, which I have
not well understood.
```

```
Date: 03/25/2002 at 12:31:34
From: Doctor Peterson
Subject: Re: binary subtaction

Hi, Robert.

This requires exactly the same trick that you use to subtract 99 from
100 in decimal; if you have never quite been solid on that, then you
will have trouble here. Here is an explanation I've given for young
children, which you may enjoy:

Borrowing in Subtraction
http://mathforum.org/dr.math/problems/christy12.1.98.html

Let's do it; I'll label the columns to make it easier:

g  f  e  d  c  b  a

1  0  1  1  0  0  0
-    1  1  0  0  1  0
---------------------
0

Now you have to borrow from column c in order to have enough in column
b. There is nothing there to borrow, so column c has to borrow from
column d. We'll do the latter first, adding binary 10 (decimal 2) to
column c:

0 10
/  /
1  0  1  1  0  0  0
-    1  1  0  0  1  0
---------------------
0

Now we can borrow from c and subtract these columns:

1 10
/  /
0 10
/  /
1  0  1  1  0  0  0
-    1  1  0  0  1  0
---------------------
0  1  1  0

The rest is easy.

If you prefer, you can write decimal digits for your borrows:

1  2
/  /
0  2
/  /
1  0  1  1  0  0  0
-    1  1  0  0  1  0
---------------------
0  1  1  0

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory

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