Rockwell Automation 1794-IE4XOE2,1794-IE8,1794-OE4,D17946.5.2 FLEX I/O ANALOG MODULE - Manual (Page 64)

Appendix
C
Publication 1794Ć6.5.2 - May 1996
Data Table Formats
Two’s complement binary is used 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