Page 195 - FUNDAMENTALS OF COMPUTER

NPP Number System, Boolean Algebra and Logic Circuits 195

F is a Boolean function which is the prod- ì`§OH$ F = (A + B ) (A. + B ) _| Xmo `moJ (A +
uct of two sums (A + B) and (A + B ). Other ex- B) VWm (A + B ) h¢ Ÿ& BZH$m JwUZ\$b {b`m h¡ & POS
amples of POS form are:
ê$n Ho$ AÝ` CXmhaU Bg àH$ma h¡…
Y = (A + B + C ) (A. + B + C )
Q = (X + Y ) (X. + Y ) (X. + Y )

F = (A + B+ C + D ) (A. + B + C + D ) (A. + B + C+ ) D
A canonical POS form is that in which each EH$ Ho$Zmo{ZH$b POS ê$n _| g^r `moJm| _| g_mZ
sum contain equal number of variables: g§»`m _| am{e`m± hmoVr h¢…
e.g. (A + B + C ) (A. + B + C ) (A. + B + C )
is a canonical POS form. But the following EH$ Ho$Zmo{ZH$b POS ñdê$n h¡ VWm {ZåZ ì`§OH$
is not a canonical POS form :
Ho$Zmo{ZH$b POS Zht h¡ …
F = (A + B + C + D ) (A. + B + C + D ) (A. + B + ) C
Problem 3.49 NPP àíZ 3.49
State whether the following expressions ~VmB`o {H$ {ZåZ SOP h¢ `m POS:
are in SOP form or POS form:
(a) F = (A + B ) (A. + B ) (A. + B ) (b) Q = D . C . B . A + D . C . B . A + D . C . B . A

(c) F = Z . Y . X + Y . X + Y . X (d) Y = R . Q . P + Q . R + . P R

(e) F = (X + Y ) (X. + Y ) (f) P = Z . F + Z . F + P . Z . F
Solution: hc:
(a) POS (b) SOP
(c) SOP (d) SOP
(e) POS (f) SOP.

3.19 Fundamental Product and Fun- 3.19 \$ÝS>m_|Q>b àmoS>ŠQ> VWm \§$S>m_|Q>b g_
damental Sum

Fundamental Product: “A Fundamental EH$ \§$S>m_|Q>b àmoS>ŠQ> dh hmoVm h¡ Omo Ma am{e`m|
Product is a product of binary variables which Ho$ EH$ {deof _mZ Ho$ {bE "1" hmoVm h¡ VWm ~mH$s gmao
is equal to ‘1’ for the specified values of the vari- _mZm| Ho$ {bE "0" hmoVm h¡ Ÿ&
ables and is equal to ‘0’ for all other values of
input variables.”
Consider two variables A and B. These vari- _mZm {H$ A VWm B Xmo Ma am{e`m± h¢, VWm BgHo$
ables may have four sets of values as shown be- Mma gå^d _mZ Bg àH$ma h¢…
low: