Find the standard Sum Of Products and Product Of Sums forms of the solution

In summary, the conversation discusses a switching network with 4 inputs and 1 output. The output Z is equal to 1 if the binary number represented by the inputs ABCD is an even number greater than 5. The problem asks for the standard POS and SOP of Z and ##\overline{Z}##. The attempt at a solution provided incorrect answers for both parts.
  • #1
Fatima Hasan
319
14

Homework Statement


A switching network has 4 inputs and a single output (Z) as shown in the figure below. The output Z is 1 iff the binary number represented by ABCD ( A is the MSB) is an even number greater than 5. Find :
a) The standard POS of Z (abbreviated form).
b) The standard SOP of ##\overline{Z}## (abbreviated form).

Homework Equations


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The Attempt at a Solution



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Could someone check my answer please ?
 

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  • #2
Could you check your answers with K-maps and share those too? Thanks. :smile:
 
  • #3
It looks like you inverted Z and not Z relative to what the problem statement asked for.
 
  • #4
berkeman said:
Could you check your answers with K-maps and share those too? Thanks. :smile:
I don't know how to solve it with K- maps , we haven't cover it yet .
 
  • #5
b) is not correct. For example, where is ##\bar{A} \bar{B} \bar{C} \bar{D}##? I think when you get b) right, you will get a) right.
 

What is the difference between Sum Of Products and Product Of Sums forms?

The Sum Of Products form is a logical expression that is obtained by taking the product of all the minterms that are equivalent to 1 in a truth table. The Product Of Sums form is a logical expression that is obtained by taking the sum of all the maxterms that are equivalent to 0 in a truth table.

How do you find the standard Sum Of Products form of a solution?

To find the standard Sum Of Products form, you need to follow these steps:

  1. Construct a truth table for the given logical expression.
  2. Identify all the rows in the truth table where the output is equal to 1.
  3. Write the minterm for each of these rows.
  4. Take the product of all the minterms to get the standard Sum Of Products form.

How do you find the standard Product Of Sums form of a solution?

To find the standard Product Of Sums form, you need to follow these steps:

  1. Construct a truth table for the given logical expression.
  2. Identify all the rows in the truth table where the output is equal to 0.
  3. Write the maxterm for each of these rows.
  4. Take the sum of all the maxterms to get the standard Product Of Sums form.

What are the advantages of using Sum Of Products and Product Of Sums forms?

The main advantage of using Sum Of Products and Product Of Sums forms is that they provide a simplified and standardized way to represent logical expressions. This makes it easier to analyze and manipulate these expressions, which is especially useful in digital circuit design and computer programming.

Can the Sum Of Products and Product Of Sums forms be used interchangeably?

Yes, the Sum Of Products and Product Of Sums forms are equivalent and can be used interchangeably. This means that any logical expression can be represented in either form and will produce the same output for the same input values.

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