Page 50 - Handout Digital Electronics

A B F
0 0 0
0 1 1
1 0 1
1 1 0

F = AB + AB
= A  B

A  B Can be written as (A+B) ( A + B ) This can be simplified by cross multiplication to:

A • A + A • B + A • B + B • B

= 0 + AB + AB + 0

= AB + AB = A  B

Note that A  B is a basic logic gate that is, Exclusive OR logic gate. So, the expression F = A  B
is a simplification of AB + AB

6.12 Drawing Logic Circuits from given Boolean Functions

Sometimes it is necessary to produce a corresponding logic circuit from a given Boolean expression.
Usually when asked to draw a logic circuit from a given Boolean expression it is not necessary to
simplify the expression and then draw the logic circuit.

Example 1

Given the Boolean expression below, draw the corresponding logic circuit: F = ( A + B )B(B + C)

Start by drawing the logic gates in parenthesis. Note that the long bar is also a bracket. So, the first logic
gate to be drawn is the OR, then the NOR, the Buffer which can be represented by a straight line (B) and
then the NAND gate, for example:

Figure 5: Logic circuit for the Boolean expression F = (A + B)B(B + C)

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