Solving Boolean Algebra Expression: Y=ABCD-ABD

In summary, the conversation discusses a possible error in a Boolean expression simplification question, where the given answer in the book may be incorrect due to a typo or a special meaning of the "-" operator. The conversation also suggests contacting the teacher or verifying the correct form of the question.
  • #1
427
2

Homework Statement



1) Simplify the following Boolean expression:
Y = ABCD – ABD


Homework Equations





The Attempt at a Solution



I simplified it in the following way:
Y = ABCD – ABD. (C + 1)
= - ABD
But the answer given in my book is ABD.
 
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  • #2
Typos are possible

Could be a typo in the back of the book. In my Discrete Math we are finding almost 20 errors per section. =o) Contact your teacher?
 
  • #3
Could you specify which textbook and which page? Thanks.

Boolean algebra deals solely in ones and zeroes. It has only three operators: addition, multiplication and negation. There can be no negative numbers. Namely, -1 is not an allowed number, so the concept of subtraction is meaningless is Boolean algebra.

Having said that, Y= ABCD – ABD has either a misprint – instead of +. In this case,
Y= ABCD + ABD = ABD(C+1)=ABD(1)=ABD

Or, possibly, – is given some special meaning.
 
  • #4
Sorry for the delayed reply. I was busy with my exams. It is a book by an Indian author. Basic Electronics by B.L.Theraja. I think u r right.The question should have been,
Y = ABD - ABCD
Isn't it?
 

1. What is Boolean algebra?

Boolean algebra is a branch of mathematics that deals with the manipulation of variables that can only have two possible values: true or false. It is used to analyze and simplify logical expressions and is widely used in computer science and digital electronics.

2. What is the purpose of solving a Boolean algebra expression?

The purpose of solving a Boolean algebra expression is to simplify a complex logical expression into a more manageable and understandable form. It allows for easier analysis and manipulation of logical statements and is essential in the design and implementation of digital circuits and computer programs.

3. How do you solve a Boolean algebra expression?

To solve a Boolean algebra expression, you need to use a set of rules and laws that govern the manipulation of Boolean variables. These include the commutative, associative, and distributive laws, as well as De Morgan's laws. By applying these rules, you can simplify the expression and reduce it to its most basic form.

4. What is the difference between simplifying and solving a Boolean algebra expression?

Simplifying a Boolean algebra expression involves reducing it to its minimal form by applying various rules and laws. On the other hand, solving a Boolean algebra expression involves finding the specific values of the variables that make the expression true or false. In other words, simplifying focuses on the structure of the expression, while solving focuses on the values of the variables.

5. How do you solve the expression Y=ABCD-ABD?

To solve the expression Y=ABCD-ABD, you can apply the distributive law to the second term, which will result in Y=ABD(C-1). Since C is a Boolean variable, its only possible values are 0 and 1. Therefore, C-1 will always evaluate to 0, making the second term equal to 0. Thus, the final simplified form of the expression is Y=ABD.

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