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# Simplification of switching functions - PowerPoint PPT Presentation

Simplification of switching functions. Simplify – why? Switching functions map to switching circuits Simpler function  simpler circuit Reduce hardware complexity Reduce size and increase speed by reducing number of gates Simplify – how? Using the postulates Ad-hoc.

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## PowerPoint Slideshow about 'Simplification of switching functions' - roger

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Presentation Transcript

• Simplify – why?

• Switching functions map to switching circuits

• Simpler function  simpler circuit

• Reduce hardware complexity

• Reduce size and increase speed by reducing number of gates

• Simplify – how?

• Using the postulates

• Simplify – what?

• SOP/POS form has products/sums and literals

• Literal: each appearance of a variable or its complement

• Minimize number of sums/products

• Reduces total gate count

• Minimize number of variables in each sum/product

• Reduces number of inputs to each gate

• PLDs have fixed # of inputs; only the number of terms need to be minimized there

• Karnaugh map (also K-map) is a graphic tool, pictorial representation of truth table

• Extension of the concepts of truth table, Venn diagram, minterm

• Transition from Venn diagram to minterm

• Adjacencies are preserved when going from c) to d)

• They are the same, only the areas are made equal in d), which preserves adjacencies

• Subscripts are dropped in e); realize that 2&3 is A; 1&3 is B

• In f) the labels change and become 0 and 1

• Each square of the K-map is 1 row of the TT

 A

B 

• Each square of the K-map is 1 row of the TT

• One to one correspondence between K-map squares and maxterms

A

A+B  M0 = m0 = AB

B

A

A+B  M3 = m3 = AB

B

• One to one correspondence between K-map squares and maxterms

A

A+B  M2 = m2 = AB

B

A

A+B  M1 = m1 = AB

B

• Constructing 3-variable K-maps

A A

B 0 1 1 0 B

0 flip  0

1 1

C = 0 C = 1

abutt

CA

B 00 01 11 10

0

1

• Constructing 3-variable K-maps

A A

B 0 1 CB 1 0

0 C = 0 00

1 01

C = 0 11

A 10

B 0 1

1 C = 1

0