Page 75 - Programmable Logic Controllers, Fifth Edition

into higher-order columns, as shown in the following
examples. EXAMPLE 10-2
Decimal Equivalent binary Subtract 111 from 100.
5 101 111
+2 + 10 −100
7 111 −011
carry Subtract 11011 from 10111.
1 11011
10 10 10 −10111
+ 3 + 11 −00100
13 11 01
carry carry
1 1 There are other methods available for doing subtraction:
26 1 1010 1’s complement
+12 + 1100 2’s complement
38 1 0 0110
The procedure for subtracting numbers using the 1’s
In arithmetic functions, the initial numeric quantities complement is as follows:
that are to be combined by subtraction are the minuend
and subtrahend. The result of the subtraction process is Step 1 Change the subtrahend to 1’s complement.
called the difference, represented as: Step 2 Add the two numbers.
A (minuend) Step 3 Remove the last carry and add it to the number
−B (subtrahend) (end-around carry).
C (difference) Decimal Binary
10 1010 1010
To subtract from larger binary numbers, subtract col- 1’s complement
umn by column, borrowing from the adjacent column − 6 −0110 +1001
when necessary. Remember that when borrowing from 4 100 10011
the adjacent column, there are now two digits, i.e., 0 bor- End-around carry +1
row 1 gives 10. 100
When there is a carry at the end of the result, the result
EXAMPLE 10-1 is positive. When there is no carry, then the result is nega-
tive and a minus sign has to be placed in front of it.
Subtract 1001 from 1101.
1101
−1001 EXAMPLE 10-3
0100 Subtract 11011 from 01101.

Subtract 0111 from 1011. 01101
1011 + − 00100 The 1’s complement
−0111 10001 There is no carry,
0100 so we take the 1’s
complement and add
the minus sign:
Binary numbers can also be negative. The procedure −01110
for this calculation is identical to that of decimal num-
bers because the smaller value is subtracted from the
larger value and a negative sign is placed in front of For subtraction using the 2’s complement, the 2’s com-
the result. plement is added instead of subtracting the numbers.

56 Chapter 3 Number Systems and Codes

pet73842_ch03_046-060.indd 56 03/11/15 3:50 PM