Page 208 - FUNDAMENTALS OF COMPUTER

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208 Fundamentals of Computers NPP

1. Drawing K-map from the Boolean func- 1. {XE JE \$bZ `m gË` Vm{bH$m H$mo XoIH$a K- _on
tion or truth table. ~ZmAmoŸ&

2. Make groups of zeros (or ones). 2. 1 `m 0 Ho$ g_yh ~ZmAmoŸ&
3. Write terms for each group. 3. àË`oH$ g_yh Ho$ {bE nX {bImoŸ&
4. Write the final minimized expression. gabrH¥$V ì`§OH$ {bImoŸ&

Groups J«wßg
Refer above to step 2. various groups of 1 s CnamoŠV {d{Y _| H«§$. 2 H$mo XoImoŸ& 1 ¶m 0 Ho$ g^r
or 0 are formed before simplifying a Boolean g_yh ~Zm gH$Vo h¢Ÿ& `o Bg àH$ma h¢Ÿ:
s
function. These groups are:
Pair noAa
This is a group of two adjacent ones in a Xmo nmg-nmg 1 Omo {H$ EH$ hr n§pŠV `m ñV§^ _|
single row or single column. Look below:
hmoVo h¢, noAa ~ZmVo h¢Ÿ& ZrMo XoI|…
1
11 1

Quad ŠdmS>
Group of four continuous ones in a single Mma 1 Ho$ g_yh Omo {H$ EH$ hr n§pŠV `m ñV§^ _| hmo
row or column or two ones just below two, `m Xmo Ho$ R>rH$ ZrMo Xmo hmo Vmo ŠdmS> ~ZmVo h¢Ÿ& ZrMo XoI|…
form a quad. Look below:
1 1 1
11 11 1 1 1
1
1
Octet Am°ŠQ>oQ>
Group of eight ones in a single row or `{X EH$ n§pŠV _| AmR> 1 `m EH$ hr ñV§^ _| AmR> 1
column, four below four or four adjacent to `m Mma Ho$ R>rH$ ZrMo Mma `m Mma Ho$ R>rH$ nmg Mma 1 hmo
four:
Vmo Am°ŠQ>oQ> ~ZVm h¡ …
1 1 111 1111 1111
1 1111
1
1 11
1 11
1 11
1 11
1
Single qgJb
An isolated one is called a single. EH$ 1 {OgHo$ Amg-nmg H$moB© Am¡a 1 Zht hmo qgJb
~ZmVm h¡Ÿ&
1