Omron CJ2 CPU UNIT SOFTWARE User Manual page 171

Additional Information
• Complements
Generally the complement of base x refers to a number produced when all digits of a given
number are subtracted from x-1 and then 1 is added to the rightmost digit. (Example: The ten's
complement of 7556 is 9999 − 7556 + 1 = 2444.) A complement is used to express a subtrac-
tion and other functions as an addition.
Example: With 8954 − 7556 = 1398, 8954 + (the ten's complement of 7556) = 8954 + 2444
= 11398. If we ignore the leftmost bit, we get a subtraction result of 1398.
• Two's Complements
A two's complement is a base-two complement. Here, we subtract all digits from 1 (2 − 1 = 1)
and add one.
Example: The two's complement of binary number 1101 is 1111 (F Hex) − 1101 (D Hex) + 1
(1 Hex) = 0011 (3 Hex). The following shows this value expressed in 4-digit hexadecimal.
The two's complement b Hex of a Hex is FFFF Hex − a Hex + 0001 Hex = b Hex. To deter-
mine the two's complement b Hex of "a Hex," use b Hex = 10000 Hex − a Hex.
Example: to determine the two's complement of 3039 Hex, use 10000 Hex − 3039 Hex =
CFC7 Hex.
Similarly use a Hex = 10000 Hex − b Hex to determine the value a Hex from the two's com-
plement b Hex.
Example: To determine the real value from the two's complement CFC7 Hex use 10000 Hex
− CFC7 Hex = 3039 Hex.
The CJ Series has two instructions: NEG(160)(2'S COMPLEMENT) and NEGL(161) (DOU-
BLE 2'S COMPLEMENT) that can be used to determine the two's complement from the true
number or to determine the true number from the two's complement.
CJ2 CPU Unit Software User's Manual
5 Understanding Programming
5
5-79