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Logical Electronic

Binary Addition

Adding binary numbers is a very simple task, and very similar to the longhand addition of decimal

numbers. As with decimal numbers, you start by adding the bits (digits) one column, or place

weight, at a time, from right to left. Unlike decimal addition, there is little to memorize in the way

of rules for the addition of binary bits

0 + 0 = 0

1 + 0 = 1

0 + 1 = 1

1 + 1 = 10

1 + 1 + 1 = 11

Just as with decimal addition, when the sum in one column is a two-bit (two-digit) number, the

least significant figure is written as part of the total sum and the most significant figure is "carried"

to the next left column. Consider the following examples:

 11     1 <--- Carry bits -----> 11

 

 

       1001101               1001001                     1000111

 +     0010010            + 0011001                  + 0010110

 ---------                  ---------                   ---------

 1011111                    1100010                     1011101

 

 

 

The addition problem on the left did not require any bits to be carried, since the sum of bits in

each column was either 1 or 0, not 10 or 11. In the other two problems, there definitely were bits to

be carried, but the process of addition is still quite simple.

As we'll see later, there are ways that electronic circuits can be built to perform this very task of

addition, by representing each bit of each binary number as a voltage signal (either "high," for a 1;

or "low" for a 0). This is the very foundation of all the arithmetic which modern digital computers

perform.


Keywords : Binary, Addition, Logic, Boolean, Algebra
Writer : delon  |
24 Nov 2006 Fri   
|  5.942 Views
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