Home Verilog Digital Design Digital Basics Python RF Basics

Legal Disclaimer

Chip Designing for ASIC/ FPGA Design engineers and Students
FULLCHIPDESIGN
Digital-logic Design...  Dream for many students… start learning front-end…
Topics @TYH :- 4G LTE Tutorial, GVIM editor, Smart-Phone, Cloud Computing
FCD
Custom Search

Feedback ? Send it to admin@fullchipdesign.com or join me at fullchip@gmail.com

Legal Disclaimer

Previous.Next.
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 K-map Ex's KMap minimization 2 var EX
Verilog Tutorial.
Digital Basics Tutorial.

Boolean Functions, equivalent truth table and gate level implementation.

Operator precedence for evaluating Boolean Expressions.

Highest           Parentheses

                            NOT

                            AND

Lowest                  OR

Boolean function example:

F1 = (x + y)z’

Where F1 is a Boolean function of binary variables and binary operators. The binary variables and operators are specified below.

Binary variables = x, y and z

Binary operators = Parentheses, NOT, AND and OR

Solving or minimization of the functions are performed in a particular precedence shown below.

Representation of Boolean function in Truth Table

X (input)
Y (input)
Z (input)
F1 (output)
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0

The truth table above lists all the variables in function as inputs (x, y and z) and the output of function as column F1.  In order to derive a gate level implementation we will need to analyze all possible combination of inputs and corresponding output.

x
y
x+y
z
Z’
(x+y)z’
A boolean function is an expression consisting for binary variables, binary operators and constants (1 or 0). The Boolean function can be used to represent a logical scenario.  Sometimes the functions can be minimized to lowest possible number of variables. In this section we will discuss boolean function with an example. We will also derive a truth-table and an equivalent  gate level implementation.   
Next, we will discuss the equivalent truth table for boolean function F1.

Next, we will discuss the equivalent gate level Implementation for Function F1.

 

The circuit is most optimized implementation of the boolean function. F1 = (x + y)z’

 

Theorems.BFunc Examples.
Solved 3 var K-map Examples
1. F(x,y,z) =sum(0,1,6,7) - Minimization.
2. F(x,y,z) =sum(0,1,4,5,6,7) - Minimization.
3. F(x,y,z) =sum(3,4,6,7) - Minimization.
4. F(x,y,z) =sum(0,1,2,3,4,5,6,7) - Minimization.
Four variable K-Map minimization example.
1. F(x,y,w, z) = (0,1,2,3,4,6,11,14)
2. F(x,y,w, z) = (0,2,4,6,12,14)
3. F(x,y,w, z) = (0,2,5,7,8,11,13,15)

Gate level minimization of above example is explained in next section. Click here

 

Interview Questions. Main, FPGA, Digital Fundamentals