Kelompok :

Fitto Martcellindo || 202131001 

Althof Zijan Putra Viandhi   202131057

               

Karnaugh Map

The Karnaugh Map is used to simplify boolean functions, by mapping the truth table in rectangular boxes whose number depends on the number of input variables.

Simplify each "1" that is 2,4,8,16... to a simple minterm.

Although Boolean algebra is a means to simplify logical statements, it is not certain that statements simplified by Boolean algebra are the simplest statements.

The minimization procedure is rather difficult to formulate because there are no clear rules to determine the manipulation steps. The Karnaugh map method provides an easy procedure.

#Format K-Map

• n  input variables will produce 2 n minterm combinations represented in rectangular form (boxes).
• A 2 variable Karnaugh map requires 2 2 or 4 squares, a 3 variable Karnaugh map has 2 3  or 8 squares, and so on.

K-Map 2 Variables

Laying out the position of the minterm tribe

 

K-Map 3 Variables

Laying out the position of the minterm tribe

Example: f = S m (0,1,2,4,6)

K-Map 4 Variables

Laying out the position of the minterm tribe

Example: f = S m (0,2,8,10,12,14 )

K-Map 5 Variables

Laying out the position of the minterm tribe

Example: f = S m (0,7,8,15,16,23,24)

 

K-Map 6 Variables

Laying out the position of the minterm tribe

Example:
f = S m (0,4,10,11,18,21,22,23,26,27,29,30,31,32,36,50, 53,54,55,58,61,62 ,63)

#Map of Karnaugh maxterm

• By mapping the truth table in rectangular boxes whose number depends on the number of input variables (variables).
• Simplification for each neighboring "0" 2,4,8,16... to a simple maxterm term.

Example: g = p M(1,3,4,5,6,7,9,11,13,15)

The Karnaugh map can be used to find the similarity of two Boolean functions.

Example: Prove equality