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Simplification of switching functionsPowerPoint Presentation

Simplification of switching functions

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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

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

- SOP/POS form has products/sums and literals

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

- Might start with rectangles initially and get the same result
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

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