Standard and Canonical Forms | Verilog | K-Map Consider the following Boolean Function: F(p,q,r) = p'q' + p'r' + qr On a separate sheet of paper complete the truth table for the function then transcribe the information requested below. Minterm р 9 r Notation Designation F Express the function in three canonical forms F(p, q, r) = F(p,q,r) = F(p, q, r) = On a separate sheet of paper prepare and complete a K-Map for the function and use it to minimize the function

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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# Standard and Canonical Forms | Verilog | K-Map

Consider the following Boolean Function:

\[ F(p, q, r) = p'q' + p'r'r + qr \]

On a separate sheet of paper complete the truth table for the function then transcribe the information requested below.

## Truth Table
| \( p \) | \( q \) | \( r \) | Notation | Designation | \( F \) |
|---------|---------|---------|----------|-------------|---------|
|         |         |         |          |             |         |
|         |         |         |          |             |         |
|         |         |         |          |             |         |
|         |         |         |          |             |         |
|         |         |         |          |             |         |
|         |         |         |          |             |         |
|         |         |         |          |             |         |
|         |         |         |          |             |         |

Express the function in three canonical forms:

\[ F(p, q, r) = \]

\[ F(p, q, r) = \]

\[ F(p, q, r) = \]

On a separate sheet of paper prepare and complete a K-Map for the function and use it to minimize the function.

## K-Map
The K-Map is shown in a grid format.

| \( yz \) | 00 | 01 | 11 | 10 |
|----------|----|----|----|----|
| **0**    |    |    |    |    |
| \( m_0 \) | 0  | c  | c  | c  |
| \( x'y'z' \) | l  | l  | l  |  |
| **1**     |    |    |    |    |
| \( r \)  | r  | r  | r  | r  |
| \( r \)  | c  | c  | c  | c  |
| \( l \)  | l  | l  | l  | l  |

Minimized function \( F(p, q, r) = \) 

---

This exercise is designed to help students understand how to convert Boolean functions into different canonical forms and minimize them using Karnaugh Maps (K-Maps).
Transcribed Image Text:# Standard and Canonical Forms | Verilog | K-Map Consider the following Boolean Function: \[ F(p, q, r) = p'q' + p'r'r + qr \] On a separate sheet of paper complete the truth table for the function then transcribe the information requested below. ## Truth Table | \( p \) | \( q \) | \( r \) | Notation | Designation | \( F \) | |---------|---------|---------|----------|-------------|---------| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Express the function in three canonical forms: \[ F(p, q, r) = \] \[ F(p, q, r) = \] \[ F(p, q, r) = \] On a separate sheet of paper prepare and complete a K-Map for the function and use it to minimize the function. ## K-Map The K-Map is shown in a grid format. | \( yz \) | 00 | 01 | 11 | 10 | |----------|----|----|----|----| | **0** | | | | | | \( m_0 \) | 0 | c | c | c | | \( x'y'z' \) | l | l | l | | | **1** | | | | | | \( r \) | r | r | r | r | | \( r \) | c | c | c | c | | \( l \) | l | l | l | l | Minimized function \( F(p, q, r) = \) --- This exercise is designed to help students understand how to convert Boolean functions into different canonical forms and minimize them using Karnaugh Maps (K-Maps).
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We have written canonical function for given Truth table 

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