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In K-map, you might find some cells filled with the letter d (or X). This d is called “Don't care". There may arise a case when for a given combination of input, we may not have a specified output, or the input combination may be invalid. The combinations for which we don't have any output expression specified are called don't care combination. When forming groups of cells, don't care conditions (d) are considered as 1, if it helps form the largest group, otherwise it is considered as 0 and are left during grouping. This is helpful if it allows us to form a larger group than would otherwise be possible without the don't cares. There is no requirement to group all or any of the don't cares. Rule: Only use the Don't cares in a group if this simplifies the logic. Based on the above note, and applying the same K-Map rules, you are asked to answer the below questions for the below 4-variable K-Map: a- Show the groups that should be considered, using the d's as 1's where necessary to obtain the optimal solution. b- Write the simplified equation of the function F. c- Find the complement (F') of the simplified F. Apply De Morgan's law and show the steps. You can keep it in the product of sum form. d- Draw the logic diagram of the simplified F using only NAND gates. F C'D' C'D CD CD' A'B' 1 1 1 A'B d d АВ d 1 d AB' d 1 1 d

In K-map, you might find some cells filled with the letter d (or X). This d is called “Don't care". There may arise a case when for a given combination of input, we may not have a specified output, or the input combination may be invalid. The combinations for which we don't have any output expression specified are called don't care combination. When forming groups of cells, don't care conditions (d) are considered as 1, if it helps form the largest group, otherwise it is considered as 0 and are left during grouping. This is helpful if it allows us to form a larger group than would otherwise be possible without the don't cares. There is no requirement to group all or any of the don't cares. Rule: Only use the Don't cares in a group if this simplifies the logic. Based on the above note, and applying the same K-Map rules, you are asked to answer the below questions for the below 4-variable K-Map: a- Show the groups that should be considered, using the d's as 1's where necessary to obtain the optimal solution. b- Write the simplified equation of the function F. c- Find the complement (F') of the simplified F. Apply De Morgan's law and show the steps. You can keep it in the product of sum form. d- Draw the logic diagram of the simplified F using only NAND gates. F C'D' C'D CD CD' A'B' 1 1 1 A'B d d АВ d 1 d AB' d 1 1 d

Database System Concepts
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
Section: Chapter Questions
Problem 1PE
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In K-map, you might find some cells filled with the letter d (or X). This d is called "Don't care". There may arise a case when for a given combination of input, we may not have a specified output, or the input combination may be invalid. The combinations for which we don't have any output expression specified are called don't care combination. When forming groups of cells, don't care conditions (d) are considered as 1, if it helps form the largest group, otherwise it is considered as 0 and are left during grouping. This is helpful if it allows us to form a larger group than would otherwise be possible without the don't cares. There is no requirement to group all or any of the don't cares. Rule: Only use the Don't cares in a group if this simplifies the logic. Based on the above note, and applying the same K-Map rules, you are asked to answer the below questions for the below 4-variable K-Map: a- Show the groups that should be considered, using the d's as 1's where necessary to obtain the optimal solution. b- Write the simplified equation of the function F. c- Find the complement (F') of the simplified F. Apply De Morgan's law and show the steps. You can keep it in the product of sum form. d- Draw the logic diagram of the simplified F using only NAND gates. F C'D' C'D CD CD' A'B' 1 1 1 A'B d d АВ d 1 d AB' d 1 d 1.
Transcribed Image Text:In K-map, you might find some cells filled with the letter d (or X). This d is called "Don't care". There may arise a case when for a given combination of input, we may not have a specified output, or the input combination may be invalid. The combinations for which we don't have any output expression specified are called don't care combination. When forming groups of cells, don't care conditions (d) are considered as 1, if it helps form the largest group, otherwise it is considered as 0 and are left during grouping. This is helpful if it allows us to form a larger group than would otherwise be possible without the don't cares. There is no requirement to group all or any of the don't cares. Rule: Only use the Don't cares in a group if this simplifies the logic. Based on the above note, and applying the same K-Map rules, you are asked to answer the below questions for the below 4-variable K-Map: a- Show the groups that should be considered, using the d's as 1's where necessary to obtain the optimal solution. b- Write the simplified equation of the function F. c- Find the complement (F') of the simplified F. Apply De Morgan's law and show the steps. You can keep it in the product of sum form. d- Draw the logic diagram of the simplified F using only NAND gates. F C'D' C'D CD CD' A'B' 1 1 1 A'B d d АВ d 1 d AB' d 1 d 1.
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