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Unformatted text preview: s, the addition table for binary arithmetic is very
simple consisting of only four entries. The complete table for binary addition is as
follows:
0+0=0
0+1=1
1+0=1
1 + 1=0 plus a carry of 1 to next higher column
Carryovers are performed in the same manner as in decimal arithmetic. Since 1 is the
largest digit in the binary number system, any sum greater than 1 requires that a digit be
carried over. For instance, 10 plus 10 binary requires the addition of two 1 's in the
second position. Since 1 + 1=0 plus a carryover of 1, the sum of 10 + 10 is 100 in binary.
By repeated use of the above rules, any two binary numbers can be added together by
adding two bits at a time. The exact procedure is illustrated with the examples given
below.
Example 5.1.
Add the binary numbers 101 and
10 in both decimal and binary form.
Solution:
Binary  Decimal
101
5
+10
+2
111
7
Add the binary numbers 10011and
1001 in both decimal and binary form.
Solution:
Binary
Carry 11
10011
+1001
11100 Decimal
Carry 1
19
+9
28 In this example of binary addition, a carry is generated for first and second columns.
Example 5.3. Add the binary numbers 100111 and 11011 in both decimal and binary form. Solution:
Binary
Decimal
Carry 11111
carry 1
100111
39
+11011
+27
1000010
66
In this example, we face a new situation (1 + 1 + 1) brought about by the carryover of 1
in the second column. This can also be handled using the same four rules for binary
addition. The addition of three 1 's can be broken up into two steps. First we add only two
1 's giving 10(1 + 1 = 10). The third 1 is now added to this result to obtain 11 (a 1 sum
with a 1 carry). So we conclude that 1 + 1 + 1 = 1 plus a carry of 1 to next higher column.
Subtraction
The principles of decimal subtraction can as well be applied to subtraction of numbers in
other bases. It consists of two steps, which are repeated for each column of the numbers.
The first step is to determine if it is necessary to borrow. If the subtrahend (the lower
digit) is larger than the minuend (the upper digit), it is necessary to borrow from...
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This document was uploaded on 04/07/2014.
 Spring '14

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