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Answers derived using Boolean Theorems and postulates.

Example 2:-

F = x + x’y

From Postulate P8

= (x + x’)(x + y)

From Postulate P3

F = x + y . Answer

Example 3:-

F = (x + y)(x +y’)

From Postulate P8

= x + yy’

From Postulate P4

= x .ans

Example 4:-

F = xy + x’z + yz

From Postulate P3

= xy + x’z + xyz + x’yz

= xy(1 + z) + x’z(1 + y)

= xy + x’z .ans

Example 5:-

F = xyz + x’y + xyz’

= xyz + x’yz + x’yz’ + xyz’

= yz + yz’

= y

Simplify following Boolean Functions:

1. F = xy + x’y + xy’

2. F = x + x’y

3. F = (x + y)(x +y’)

4. F = xy + x’z + yz

5. F = xyz + x’y + xyz’

Example 1:-

F = xy + x’y + xy’

From Theorem T1

= xy + xy + x’y + xy’

= y(x + x’) + x(y + y’)

From Postulate P3

= y + x . Answer

Access previous topic for details on Boolean Functions, equivalent truth table and gate level implementation. Examples are discussed next.

Exercise :-

Digital Logic fundamentals topics

Digital basics tutorial

Binary number discussion, 1 and 2 complement discussion,

Binary arithmetic, Signed Magnitude, overflow, examples

Gray coding, Binary coded digital (BCD) coding, BCD addition

Digital logic gates basic (AND, OR, XOR, NOT) and derived (NAND, NOR and XNOR). Drive XOR from NAND gates. Drive XOR from NOR gates

Discussion of Boolean Algebra with examples.

Duality Principle, Huntington Postulates, Theorems of Boolean Algebra - discussion with examples,

Boolean Functions,

Canonical and Standard Forms, Minterms and Maxterms

Sum of Minterms, Product of Maxterms or Canonical Forms,

Karnaugh map or K-map discussion 2, 3, ,4 and 5 var’s

Prime Implicant and Gate level minimization examples.

Digital basics tutorial

Binary number discussion, 1 and 2 complement discussion,

Binary arithmetic, Signed Magnitude, overflow, examples

Gray coding, Binary coded digital (BCD) coding, BCD addition

Digital logic gates basic (AND, OR, XOR, NOT) and derived (NAND, NOR and XNOR). Drive XOR from NAND gates. Drive XOR from NOR gates

Discussion of Boolean Algebra with examples.

Duality Principle, Huntington Postulates, Theorems of Boolean Algebra -

Canonical and Standard Forms, Minterms and Maxterms

Sum of Minterms, Product of Maxterms or Canonical Forms,

Karnaugh map or K-

Prime Implicant and Gate level minimization examples.

Resources

Verilog RTL code examples for front-end chip design.

Digital Design Topics

Half-adder , full-adder ,

Adder-sub tractor

Stack Organization - LIFO, RPN

Parity Generation and error checking

Binary multiplier circuit.

CMOS introduction

Digital fundamentals -

RTL coding guidelines. ICG cell, Assertions, $assertkill, levels. Chandle

Pipeline vs. Parallel processing.

Verilog RTL code examples for front-

Half-

Adder-

Stack Organization -

Binary multiplier circuit.

CMOS introduction

Digital fundamentals -

RTL coding guidelines. ICG cell, Assertions, $assertkill, levels. Chandle

Pipeline vs. Parallel processing.

Interview Questions. Main, FPGA, Digital Fundamentals