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Islamic University

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Simplifcation o Boolean Functions: An implementation o a Boolean

Function requires the use o logic

gates. A smaller number o gates, with each

gate (other then Inerter! haing lessnumber o inputs, ma" re#uce the cost

o the implementation.

 $here are 2 metho#s or simplifcationo Boolean unctions.

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%

Simplifcation o Boolean Functions:

 $wo &etho#s  $he algebraic metho# b" using I#entities  $he graphical metho# b" using 'arnaugh &ap

metho#

 $he 'map metho# is eas" an#straightorwar#. $his metho# was frstpropose# b" )eitch an# later slightl"mo#ife# b" 'arnaugh

A 'map or a unction o n ariables consists o 2n cells, an#,

in eer" row an# column, two a#*acent cellsshoul# #i+er in the alue o onl" one o the

logic ariables.

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-amples o '&aps:

-amples:

/ell numbers are written in the cells.

  2ariable 'map

0ote that A appears prime# in row 1 an# unprime# in

row . Similarl" B appears prime# in column 1 an#

unprime# in column .

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 $he unction F3AB

 $he unction F3A4B

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%)ariable '&ap:   %ariable 'map

 $here are 7 minterms or % ariables. $hereore a threeariable '&apconsists o eight squares.

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ariable 'map ariable 'map

Four ariable 'arnaugh map contains 2, 

3 6 squares.

m0   m1   m3   m2

m4 m5 m8 m6

m12 m% m5 m

m8 m9 m m1

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 $he rows an# columns in the aboe '&ap arenumbere# in a reecte# co#e sequence, withonl" one #igit changing its alue between two

a#*acent rows or columns.

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;art F 3 A<B</< 4 A<B</ 4 AB/< 4 AB/

  3 111 4 11414

&interm shorthan# equation3=(1,,6,8!

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F3AB4A<B<

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>ogic ?iagram

AB

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;art 2: control o pseu#obit binar" co#es

2

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1 1 1 1

1 1 1 1

1 1

111

1

11 1 1

AB

/?

@3AB4A/

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0A0? $-/0>CD

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>ogic #iagram

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