Page 199 - FUNDAMENTALS OF COMPUTER

NPP Number System, Boolean Algebra and Logic Circuits 199

There are two 1s in the output. First ‘1’ cor- AmCQ>nwQ> _| Xmo "1" h¢ AV… Xmo {_ÝQ>_© àmßV hmoJr Ÿ&
responds to (01) and therefore the fundamental àW_ {_ÝQ>_© (01) Ho$ gmnoj hmoJr VWm {ÛVr` (11) Ho$
product is .A B . Similarly, for second ‘1’ the fun- gmnoj `o .A B VWm A.B hmoJr Ÿ&
damental product is A.B. Thus, the expression
Y has two minterms, .A B and A.B.
Minterms are represented by m where n {_ÝQ>_© H$mo m Ho$ ê$n _| àX{e©V H$aVo h¢ Ohm± na
n
n
is the decimal equivalent of the corresponding n g§~§{YV ~mBZar g§»`m H$m Xe_bd Vwë` h¡Ÿ& O¡go
binary number. In the above example the first Cnamoº$ Vm{bH$m _| àW_ BZnwQ> ~mBZar g§»`m 01 BgH$m
binary value is (01). Its decimal is 1. Thus, the S>ogr_b 1 h¡Ÿ& AV: {_ZQ>_© A H$mo m Ho$ ê$n go
minterm .A B can be represented as m . There- àñVwV {H$`m Om gH$Vm h¡Ÿ& AV: B . 1
1
fore:
m = A B . and Similarly, m = A.B
1
3
Problem 3.52 àíZ 3.52
For the given table identify all the Vm{bH$m hoVw gmar {_ÝQ>_© àmßV H$s{OE…
minterms:
B
A NPP C F
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 1
Solution: hc:
There are four 1s in the output. Therefore My±{H$ AmCQ>nwQ> _| Mma 1 h¢ AV… Mma {_ÝQ>_©
the minterms are:
{ZåZmZwgma hmoJr…
m = C . B . A , m = C . B . A ,
1
3
m = C . B . A , m = C . B . A
7
4
3.21 Finding an expression for the 3.21 AmCQ>nwQ> hoVw ì`§OH$ kmV H$aZm
output
Given the truth table, we can write the ex- `{X Vm{bH$m Xr JB© hmo Vmo AmCQ>nwQ> hoVw ì`§OH$
pression for the output variable. For this pur- AmgmZr go kmV {H$`m Om gH$Vm h¡Ÿ& BgHo$ {b`o gmao
pose, find all the minterms and add logically. {_ÝQ>_© {ZH$mbH$a CZH$mo Omo‹S>Zm hmoVm h¡Ÿ& AV… AmCQ>nwQ>
Thus, “The output expression is logical sum of gmao {_ÝQ>_m] H$m Vm{H©$H$ `moJ hmoVm h¡Ÿ& {ZåZ Vm{bH$m H$mo
all the minterms.” e.g. Consider the following XoImo…
truth table: