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Unit 3: Boolean Algebra

Notes
Utilizing theorem (15), we can replace A + AB by A + B, so
x = CD(A + B)

= ACD + BCD

Simplify the Boolean expression F = C (B + C) (A + B + C).

Boolean logic forms are the basis for computation in modern binary computer
systems.

Self Assessment
Choose the correct answer:
1. Give the relationship that represents the dual of the Boolean property A + 1 = 1.

(a) A * 1 = 1 (b) A * 0 = 0
(c) A + 0 = 0 (d) A * A = A
2. The best definition of a literal is:
(a) A Boolean variable (b) The complement of a Boolean variable
(c) 1 or 2 (d) A Boolean variable interpreted literally
3. On simplifying the Boolean expression (A + B + C)(D + E)’ + (A + B + C)(D + E), the best
answer is:

(a) A + B + C (b) D + E
(c) A’B’C’ (d) D’E’
4. What is the Boolean expression for the logic circuit shown below:

–
(a) C(A+B)DE (b) [C(A+B)D+E]
–
(c) [[C(A+B)]D]E (d) ABCDE

3.3 DeMorgan’s Theorems

Two of the most important theorems of Boolean algebra were contributed by a great mathematician
named DeMorgan. DeMorgan’s theorems are extremely useful in simplifying expressions in which
a product or sum of variables is inverted.

DeMorgan’s first theorems: In words, the complement of a logical sum equals the logical product
of the complements. In the term of circuits, a NOR gate equals a bubbled AND gate.
DeMorgan’s second theorems: In words, the complement of a logical product equals the logical sum
equals the complements. In the term of circuits, a NAND gate is equivalent to a bubbled OR gate.
The two theorems are:
1. (x + ) y = xy

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