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Boolean Function in Sum of Minterms

Any boolean function can be represented in SOM by following a 2 step approach discussed below.

Step1: Represent the minterms for a function by decimal 1 in column 4 of table below. Refer minterms from here

Step2: Add (or take binary OR) all the minterms in column 5 of table to represent the function.

The Function of Minterms from above table is represented below

F = x’y’z + x’yz’ + xy’z + xyz’ + xyz

Example: Represent F = x + yz + xy in Sum of minterms.

F = x (y + y’)(z + z’) + yz (x + x’) + xy (z + z’)

= xyz + xyz’ + xy’z + xy’z’ + xyz + x’yz + xyz + xyz’

= xyz + xyz’ + xy’z + xy’z’ + x’yz

Answer. Digital basics tutorial from here

x

y

z

Minterm in Function

Minterms

0

0

0

0

0

0

1

1

x’y’z

0

1

0

1

x’yz’

0

1

1

0

1

0

0

0

1

0

1

1

xy’z

1

1

0

1

xyz’

1

1

1

1

xyz

Digital Logic fundamentals topics @ fcd

Binary number discussion, 1 and 2 complement discussion, and tutorials of logic design.

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.

Binary number discussion, 1 and 2 complement discussion, and tutorials of logic design.

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 -

Arithmetic, logical and shift micro-ops.

Binary t o Gray codeconversion

Readmemh, Readmemb. Random numbers

Memory Implementation - sync Ram and Testbench

Readmemh, Readmemb. Random numbers

Memory Implementation -

Sum of Minterms or SOM is an equivalent statement of Sum of Standard products.

Truth Table of three variable example below.

Details on minterms and maxterms from here.

LTE - Long Term Evolution topics here