Simplification of switching functions

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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
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
Simplification of switching functions
• 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 maps
• 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
Karnaugh maps
• 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
Karnaugh maps

 A

B 

• Each square of the K-map is 1 row of the TT
Karnaugh maps
• One to one correspondence between K-map squares and maxterms

A

A+B  M0 = m0 = AB

B

A

A+B  M3 = m3 = AB

B

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

A

A+B  M2 = m2 = AB

B

A

A+B  M1 = m1 = AB

B

3-variable K-maps
• 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

3-variable K-maps
• 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