Page 57 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes (b) a NAND and an OR gate with inverted inputs
(c) an AND and a NOR gate with inverted inputs
(d) a NOR and a NAND gate with inverted inputs
6. The commutative law of Boolean addition states that A + B = A × B.
(a) True (b) False
7. The systematic reduction of logic circuits is accomplished by:
(a) using Boolean algebra (b) symbolic reduction

(c) TTL logic (d) using a truth table
8. An AND gate with schematic “bubbles” on its inputs performs the same function as a
(n) ................ gate.
(a) NOT (b) OR
(c) NOR (d) NAND

3.4 Summary

• Boolean algebra are truth tables, canonical representation, of Boolean functions, Boolean
function simplification, logic design, combinatorial and sequential circuits, and hardware/
software equivalence.
• Multiplication is valid in Boolean algebra, and thankfully it is the same as in real-number
algebra: anything multiplied by 0 is 0, and anything multiplied by 1 remains unchanged.
• Boolean theorems (rules) that help us to simplify logic expressions and logic circuits.

• Sum-Of-Products expressions are easy to generate from truth tables. All we have to do is
examine the truth table for any rows where the output is “high” (1), and write a Boolean
product term that would equal a value of 1 given those input conditions.
• Products-Of-Sums standard Boolean forms are powerful tools when applied to truth tables.
They allow us to derive a Boolean expression and, ultimately, an actual logic circuit from
nothing but a truth table, which is a written specification for what we want a logic circuit
to do.

3.5 Keywords

Boolean algebra: It is used to help analyze a logic circuit and express its operation mathematically.
Boolean quantities: It has led to the simple rules of addition and multiplication, and has excluded
both subtraction and division as valid arithmetic operations.

Boolean theorem: It is useful in simplifying a logic expression—that is, in reducing the number
of terms in the expression.

DeMorgan’s theorem: These are extremely useful in simplifying expressions in which a product
or sum of variables is inverted.

Distributive law: It states that an expression can be expanded by multiplying term by term just
the same as in ordinary algebra.

1. Construct an OR gate connecting NAND gate.
2. Prepare an OR gate using AND and NOR gate.

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