Page 197 - FUNDAMENTALS OF COMPUTER

NPP Number System, Boolean Algebra and Logic Circuits 197

0 1 0 C . B . A
0 1 1 C . B . A

1 0 0 C . B . A
1 0 1 C . B . A

1 1 0 C . B . A
1 1 1 A.B.C
Fundamental Sum \§$S>m_|Q>b `moJ
“Fundamental sum for given values of vari- `h EH$ Eogm `moJ hmoVm h¡ {OgH$m _mZ {H$gr {X`o JE
ables is a sum formed such that it is equal to ‘0’ _mZm| hoVw '0' hmoVm h¡ VWm ~mH$s AÝ` _mZm| hoVw '1' .
for that set of values only and for all other sets
it is equal to ‘1’.”
Consider two variables A and B. These vari- O¡go Xmo am{e`m| A VWm B Ho$ Mma gå^d _mZ ZrMo
ables have four sets of values as show in the Vm{cH$m _| h¡ …
table: NPP
A B
0 0
0 1
1 0
1 1
Consider the third combination (A = 1, O¡go V¥Vr` n§{º$ _| (A = 1 VWm B = 0) h¡, Vmo BgHo$
B = 0), the fundamental sum is: {b`o \§$S>m_|Q>b `moJ Bg àH$ma hmoJm…

(A + B )
The following steps are taken to form a fun- {ZåZmZwgma {H$gr \§$S>m_|Q>b `moJ H$mo ~Zm`m OmVm
damental sum: h¡…
1. Put a bar over a variable which is equal to 1. {Og am{e H$m _mZ '1' h¡, CgHo$ D$na ~ma (-)
‘1’. bJmAmo& AÝ`Wm ZhtŸ&
2. Do not put a bar over a variable which is 2. AJa am{e H$m ‘mZ 0 h¡ Vmo ~ma Z bJmE&
equal to ‘0’.
3. Put a + (Plus) sign between all the variables 3. Cnamoº$mZwgma àmßV g^r am{e`m| Ho$ _Ü` `moJ (+)
formed with the help of step 1 and 2. H$m {M• bJmAmoŸ&
Applying the above procedure four funda- Cnamoº$ {d{Y H$m Cn`moJ H$a h_ {ZåZmZwgma
mental sums are obtained as shown below in \§$S>m_|Q>b `moJ àmßV H$a gH$Vo h¢…
the table: