09 - Manipulate Boolean Expressions

 1. Minimising terms and expressions can be important because electrical circuits consist of individual components that are implemented for each term for a given expression. This allows designers to

  make use of far more components, thereby increasing efficiency

  make use of fewer components, thus reducing the cost of a particular system.

  make use of fewer but larger components, thereby increasing the cost of the system

  make use of a greater number of components, thereby increasing speed

 2. All Boolean expressions, regardless of their form, can be converted into either of two standard forms:
The sum-of-products (SOP) form
The product-of-sums (POS) form



 3. A sum-of-products form is when two or more product terms are summed by Boolean addition e.g.
Note: The opposite is when two or 
more sum terms are multiplied, the
result expression is a
product-of-sums (POS)


  AB x AB


  AB + ABC

 4. In the following example, which of the options given is acceptable/okay?
In an SOP form, a
single overbar cannot
extend over more than
one variable; however,
more than one variable
in a term can have an

  1 is OKAY, 2 is not

  2 is OKAY, 1 is not

  Neither are acceptab;e

  Both are acceptabe

 5. The output of AND gates in SUM of Product (SOP) is connected to OR gates.