Rockwell Automation 1771-IFE , D17716.5.90 USER MNL. ANALOG INPUT Module - Manual (Page 54)

Data Formats
Appendix C
C-3
Two’s complement binary is used with PLC-3 processors when performing
mathematical calculations internal to the processor. To complement a
number means to change it to a negative number. For example, the
following binary number is equal to decimal 22.
10110
2
= 22
10
First, the two’s complement method places an extra bit (sign bit) in the
left-most position, and lets this bit determine whether the number is
positive or negative. The number is positive if the sign bit is 0 and negative
if the sign bit is 1. Using the complement method:
0 10110 = 22
To get the negative using the two’s complement method, you must invert
each bit from right to left after the first “1” is detected.
In the above example:
0 10110 = +22
Its two’s complement would be:
1 01010 = –22
Note that in the above representation for +22, starting from the right, the
first digit is a 0 so it is not inverted; the second digit is a 1 so it is not
inverted. All digits after this one are inverted.
If a negative number is given in two’s complement, its complement (a
positive number) is found in the same way:
1 10010 = –14
0 01110 = +14
All bits from right to left are inverted after the first “1” is detected.
The two’s complement of 0 is not found, since no first “1” is ever
encountered in the number. The two’s complement of 0 then is still 0.
Two's Complement Binary