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Binary Numbers 1s_complement 2s_complement Binary Subtraction Binary Sub. Ex's Sign_magnitude SignM EX Gray Coding BCD coding Digital gates NAND NOR & XNOR Theorems Boolean Functions BFunc Examples Minterm Maxterm Sum of Minterms Prdt of Maxterms 2 var K-map 3 var K-map 4 var K-map 5 var K-map Prime Implicant PI example

3 - variable Karnaugh map (K-map)

Truth Table

3 variable K– map

00

01

4

5

11

10

7

6

 

x’y’z’

 

 

x’y’z

 

 

x’yz

 

 

x’yz’

 

 

xy’z’

 

 

xy’z

 

 

xyz

 

 

xyz’

 

 

K-map location Number

 

 

x

 

 

y

 

 

z

 

 

Output Function

 

 

0

 

 

0

 

 

0

 

 

0

 

 

x’y’z’

 

 

1

 

 

0

 

 

0

 

 

1

 

 

x’y’z

 

 

2

 

 

0

 

 

1

 

 

0

 

 

x’yz’

 

 

3

 

 

0

 

 

1

 

 

1

 

 

x’yz

 

 

4

 

 

1

 

 

0

 

 

0

 

 

xy’z’

 

 

5

 

 

1

 

 

0

 

 

1

 

 

xy’z

 

 

6

 

 

1

 

 

1

 

 

0

 

 

xyz’

 

 

7

 

 

1

 

 

1

 

 

1

 

 

xyz

 

0

1

x

yz

Interview Questions. Main, FPGA, Digital Fundamentals