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

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

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

  make use of far more components, thereby increasing efficiency

 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 + ABC


  AB x AB


 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

  Neither are acceptab;e

  2 is OKAY, 1 is not

  Both are acceptabe

  1 is OKAY, 2 is not

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