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NPP Number System, Boolean Algebra and Logic Circuits 285
us it is very easy to identify the condition for ~Vm gH$Vo h¢ & `{X Xmo YZmË_H$ g§»`mAm| H$mo Omo‹S>Zo go
overflow. The resulting sign bit would differ n[aUm_ F$UmË_H$ AmE `m BgH$m CëQ>m hmo Vmo `h
from the sign bits of integers which are added.
This is called sign reversal. That is the sum of Amodaâbmo H$s pñW{V h¡Ÿ& Bgo gmBZ [aìhg©b H$hVo h¢Ÿ&
two positive numbers would be a negative AWm©V² n[aUm_r g§»`m H$m {MÝh Omo‹S>r JB© g§»`mAm| Ho$
number and vice-versa. {MÝh go {dnarV AmEJm &
But computer circuit uses C (carry in to bo{H$Z H$åß`yQ>a n[anW C VWm C H$s ghm`Vm
in
in
out
the sign bits) and C out (carry-out to the sign bit) go Amodaâbmo H$m nVm bJmVm h¡Ÿ& AJa `h XmoZm| {~Q>|
to determine the condition for overflow. If both g_mZ h¢ Vmo Amodaâbmo Zht h¡ AV… XmoZm| na XOR H$s
are similar, there is no overflow. That is the
reason why both are Exclusive ORed to get {H«$`m H$s OmVr h¡…
overflow bit:
OF = C ⊕ C out
in
OF → Overflow Flag. The overflow flag Ohm± OF → Amodaâbmo âboJ h¡ Ÿ& âboJ V^r goQ>
sets if both C and C out are different, indicating hmoVm h¡ (AWm©V² 1) O~ C VWm C AbJ-AbJ h¡ Ÿ&
in
overflow condition. Consider an example: in out
{ZåZ CXmhaU H$mo XoImo…
(+5) + (+6)
C out C in
0 1
( 5) → 0 1 0 1
+
+
( 6) → + 0 1 1 0
1 0 11
Sign Reversal
OF = C ⊕ C out = 1 ⊕ 0 = 1
in
This is a case of overflow.
2's Complement Subtraction (Signed) gmBÝS> 2's H$m°påßb_|Q> KQ>md
Suppose the problem of signed subtraction {ZåZ KQ>md H$s g_ñ`m H$mo XoImo…
is
(±A) – (±B)
If we take 2's complement of (±B) it will be `{X h_ (± B) H$m 2's H$m°påßb_|Q> b| Vmo dh ( B )
converted to ( B ) or in other words subtraction hmo OmEJm Ÿ& Bg Vah go KQ>md Omo‹S> _| n[ad{V©V hmo OmEJm
sign (–) would be changed to addition (+). Now
it becomes the 2's complement addition Ÿ& Omo‹S> H$s g_ñ`m h_ nhbo hr n‹T> MwHo$ h¢ Ÿ& g_w{MV
problem. Add both numbers and neglect any à{V{Z{YËd Ho$ níMmV² ~mBZar g§»`mAm| H$mo Omo‹S>Vo h¢ VWm
end carry. Consider the following. Example: A§{V_ hm{gb H$mo N>mo‹S> XoVo h¢ Ÿ& CXmhaU…
(+15) – (–17)
