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What you need to know
What you need to know
(a) Define problems using Boolean logic.
(b) Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions.
(c) Use the following rules to derive or simplify statements in Boolean algebra: De Morgan’s Laws, distribution, association, commutation, double negation.
(d) Using logic gate diagrams and truth tables.
(e)The logic associated with D type flip flops, half and full adders.
Boolean Logic
Boolean Logic
Karnaugh Maps
Karnaugh Maps
Also known as K-Maps, these are a way of simplifying Boolean algebra
Simplifying an expression
Simplifying an expression
Example Expression: A ∨ (A ∧ B)
Example Expression: A ∨ (A ∧ B)
1. Divide the expression into the two parts on either side of the OR symbol
2. Write a 1 in each square for which one side of the expression is true (A)
3. Write a 1 in each square for which the other side is true (A ∧ B)
4. Draw a box around the group of adjacent 1s, think about what expression this represents (in this case A, the whole expression can be simplified down to just A)
Rules to remember:
Rules to remember:
We group items in groups of 1, 2, 4 or 8
NEVER 3, 5, 6, 7
Groups can overlap
Each group should be as large as possible
Each 1 must be included in at least one group
Groups can wrap and still count as a single group
This is an example of a 4 variable K-map. The green group represents
(¬B ∧ ¬C ∧ ¬D) and wraps around the 1st column. The purple row reperent
(¬A ∧ B) as the values for A 0 are set to 1 so this means NOT and the B 1 are set to 1 which are True.
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