Page 196 - FUNDAMENTALS OF COMPUTER

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196 Fundamentals of Computers NPP

A B
0 0
0 1
1 0
1 1
Consider the first set (0, 0) since A = 0 write àW_ _mZ (0, 0) H$mo XoImo My±{H$ A = 0 h¡ AV… A
A and B = 0, write B . Make a product: {bImo Bgr Vah B {bIH$a JwUm H$amo…

B . A B . A
This product is equal to ‘1’ for A = 0, B = 0 A = 0 VWm B = 0 aIZo na Bg JwUZ\$b H$m _mZ
only and is equal ‘0’ for all other sets of values "1" AmVm h¡ VWm H$moB© AÝ` _mZ aIZo na h_oem eyÝ` AmVm
of A, B. Thus, the technique to make a funda- h¡ Ÿ& \§$S>m_|Q>b àmoS>ŠQ> ~ZmZo H$s {d{Y Bg àH$ma h¡…
mental product is as follows:
1. Put a bar if the variable is equal to ‘0’. 1. `{X am{e H$m _mZ eyÝ` h¡, Vmo CgHo$ D$na ~ma
(-) bJmAmo&
2. Do not put a bar if the value of the 2. ~ma Z bJm`| `[X d¡[aE~b H$m _mZ 1 h¡Ÿ&
variable is equal to ‘1’.
3. Put dots between all the variables formed 3. MaU 1 VWm 2 go àmßV g^r am{e`m| Ho$ _Ü` S>m°Q>
with step 1 and 2. (.) bJmAmoŸ&
Applying above method to all combina- Cnamoº$ Vm{bH$m hoVw Mma \§$S>m_|Q>b àmoS>ŠQ> Bg
tions of two variable A and B we can obtain four àH$ma àmßV H$a gH$Vo h¢…
fundamental products as shown in the table:
A B Fundamental products
0 0 B . A

0 1 A B .
1 0 B . A
1 1 A.B
Problem 3.50 àíZ 3.50
Find all the fundamental products for the A, B VWm C Ho$ gmao \§$S>m_|Q>b àmoS>ŠQ> {ZH$mbmo…
three variables A, B and C:
Solution: hc:
Three variable have 2 = 8 sets of values. VrZ am{e`m| Ho$ 8 goQ> hm|Jo & VrZ am{e`m| hoVw \§$S>m_|Q>b
3
Eight fundamental products are as follows: àmoS>ŠQ> Bg àH$ma h¢…
A B C Fundamental Products

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