Filter
Top Products
FX Series Programmable Controllers Devices in Detail 4
4-45
4.14.4 Two’s Compliment
Pro
g
rammable controllers, computers etc, use a format called 2’s compliment. This is a
mathematical procedure which is more suited to the micro processors operational hardware
requirements. It is used to represent ne
g
ative numbers and to perform subtraction operations.
The procedure is ver
y
simple, in the followin
g
example “15 - 7” is
g
oin
g
to be solved:
Step1: Find the binar
y
values (this example uses 8 bits)
15 = 00001111
7 = 00000111
Step2: Find the inversion of the value to be subtracted.
Procedure
: invert all 1ís to 0ís and all 0ís to 1’s.
7 = 00000111
Inverted 7 = 11111000
Step3: Add 1 to the inverted number.
Procedure:
add 1 to the ri
g
ht hand most bit. Remember this is binar
y
addition hence, when a
value of 2 is obtained 1 is moved in to the next left hand position and the remainder is set to 0
(zero);
Inverted7
11111000
Additional1
00000001
Answer
11111001
This result is actuall
y
the same as the ne
g
ative value for 7 i.e. -7.
Step4:
Add the answer to the number the subtraction is bein
g
made from (i.e. 15).
Procedure:
Remember 1+1 = 0 carr
y
1 in base 2 (binar
y
).
Ori
g
inal value15
00001111
Answer found in step3
11111001
Solution
(1)00001000
The “(1)” is a carried “1” and is i
g
nored as this example is onl
y
dealin
g
with 8 bits.
Step 5:
Convert the answer back.
00001000 = 8
The answer is positive because the MSB (the most left hand bit) is a 0 (zero). If a quick mental
check is made of the problem it is indeed found that “15-7 = 8”.
In fact no subtraction has taken place. Each of the steps has either converted some data or
performed an addition. Yet the answer is correct 15 - 7 is 8. This example calculation was
based on 8 bit numbers but it will work equall
y
well on an
y
other quantit
y
of bits.