Binary SubtractionDate: 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/ |
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