They connect your search words together to either narrow or broaden your set of results. The three basic boolean operators are: AND, OR, and NOT.

Boolean algebra makes it possible to use the same kinds of algebraic techniques we use to solve normal equations involving numbers to establish logical relationships. By solving Boolean equations, logicians can more easily see when one combination of propositions logically leads to another.

Boolean algebra is used frequently in computer programming.

Programs use simple comparisons to help make decisions. Boolean logic is a form of algebra where all values are either True or False. These values of true and false are used to test the conditions that selection and iteration are based around.

Boolean algebra is a branch of mathematics that deals with operations on logical values with binary variables. The Boolean variables are represented as binary numbers to represent truths: 1 = true and 0 = false. The primary modern use of Boolean algebra is in computer programming languages.

The SOP (Sum of Product) and POS (Product of Sum) are the methods for deducing a particular logic function. In other words, these are the ways to represent the deduced reduced logic function. Conversely, POS produces a logical expression comprised of the AND of the multiple OR terms.

Min-terms are represented with ‘m’, they are the product(AND operation) of boolean variables either in normal form or complemented form.

1. Therefore, SOP is sum of minterms and is represented as: F in SOP = m(0, 3)
2. X (SOP) = m(1, 3, 6)
3. Therefore, POS is product of maxterms and is represented as:

To convert the POS form into SOP form, first we should change the Π to Σ and then write the numeric indexes of missing variables of the given Boolean function. Step 2: writing the missing indexes of the terms, 000, 001, 100, 110, and 111. Now write the product form for these noted terms.

For SOP, we pair 1 and write the equation of pairing in SOP while that can be converted into POS by pairing 0 in it and writing the equation in POS form. For example, for SOP if we write x⋅y⋅z then for pos we write x+y+z.

because all terms should be zero for F to be zero, whereas any of the terms in POS being one results in F to be one. Thus it is known as MINTERM (minimum one term!)

Conversion of SOP form to standard SOP form or Canonical SOP form

1. Multiply each non-standard product term by the sum of its missing variable and its complement.
2. Repeat step 1, until all resulting product terms contain all variables.
3. For each missing variable in the function, the number of product terms doubles.

The Sum of Product (SOP) expression comes from the fact that two or more products (AND) are summed (OR) together. That is the outputs from two or more AND gates are connected to the input of an OR gate so that they are effectively OR’ed together to create the final AND-OR logical output.

Two dual canonical forms of any Boolean function are a “sum of minterms” and a “product of maxterms.” The term “Sum of Products” (SoP or SOP) is widely used for the canonical form that is a disjunction (OR) of minterms.

Standard SoP form means Standard Sum of Products form. In this form, each product term need not contain all literals. So, the product terms may or may not be the min terms. Therefore, the Standard SoP form is the simplified form of canonical SoP form.

3. Which of the following is an incorrect SOP expression? Explanation: The second expression is incorrect because it consists of two maxterms ANDed together. This makes it a POS or the product of sum expression.

An SOP is a procedure specific to your operation that describes the activities necessary to complete tasks in accordance with industry regulations, provincial laws or even just your own standards for running your business. Any document that is a “how to” falls into the category of procedures.

Here is a simple SOP for a bank to verify the identity of a walk in costumer: Purpose: This procedure describes the steps required to verify customer identity. Scope: This procedure applies to any walk-in customer or a customer at the drive-by windows of all branches of ACME Bank.

Discussion Forum

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

Multiplying Algebraic Expressions:

1. The product two factors with the same signs will be positive, and the outcome of multiplying two terms with two, unlike signs, will be negative.
2. If x is variable and a, b are positive integers then, (xa * xb) = x. (m +n)

To simplify any algebraic expression, the following are the basic rules and steps:

1. Remove any grouping symbol such as brackets and parentheses by multiplying factors.
2. Use the exponent rule to remove grouping if the terms are containing exponents.
3. Combine the like terms by addition or subtraction.
4. Combine the constants.

Algebra helps in the representation of problems or situations as mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression. One simple example of algebra is 2x + 4 = 8. …

Here is a list of Algebraic formulas – a2 – b2 = (a – b)(a + b) (a + b)2 = a2 + 2ab + b2. a2 + b2 = (a + b)2 – 2ab. (a – b)2 = a2 – 2ab + b2.

There are 3 main types of algebraic expressions which include:

• Monomial Expression.
• Binomial Expression.
• Polynomial Expression.

Algebra is divided into different sub-branches such as elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.

In algebra, terms are the values on which the mathematical operations take place in an expression. A term can be a constant or a variable or both in an expression. In the expression, 3a + 8, 3a and 8 are terms.