Digital Logic Design Basics

Logic gates and Boolean Algebra

_______ are circuits that perform logical operations based on input signals. They are used in digital systems to manipulate binary data. Each _______ has a truth table that determines its output based on the input values.

Logic gates

What is the output of an XOR gate when both inputs are different?

The output of an XOR gate is HIGH (1) when the inputs are different.

What is the output of an XOR gate when both inputs are the same?

The output of an XOR gate is LOW (0) when the inputs are the same.

Where can we use XOR gates?

XOR gates can be used in half-adders, full-adders, and subtractors.

Is XOR an odd or an even function? Explain.

XOR is an odd function meaning the output of an XOR gate is 1 if the input variables have an odd number of ones.

What is the output of an XNOR gate when both inputs are the same?

The output of an XNOR gate is HIGH (1) when both inputs are the same, either both are HIGH (1) or both are LOW (0).

—————— is used to analyze and simplify logic circuits. It uses binary numbers only.

Boolean Algebra

The complement of a variable is represented by an ———.

overbar

What does the commutative law in Boolean Algebra state?

Changing the sequence of the variables doesn’t affect the output of a logic circuit.

What does the associative law in Boolean Algebra state?

It states that the order in which the logic operations are performed is irrelevant as their effect is the same.

—————— of a variable results in the original variable itself.

Double inversion

What does the absorption law state?

It states that A’B + A = B + A

What does DeMorgan’s First Theorem state?

It states that a NAND gate is equivalent to a Bubbled OR gate.

What does DeMorgan’s Second Theorem state?

It states that a NOR gate is equivalent to a Bubbled AND gate.

Functions up to 5 variables can be simplified by the ————.

map method

What do designers of digital circuits use for complex Boolean functions?

Computer minimization programs

What are AND terms called?

minterms or standard products

When is a variable primed and unprimed in the case of AND terms?

A variable is primed if the corresponding bit of the binary number is a 0 and unprimed if the corresponding bit of the binary number is a 1.

What are OR terms called?

maxterms or standard sums

When is a variable primed and unprimed in the case of OR terms?

A variable is primed if the corresponding bit of the binary number is a 1 and unprimed if the corresponding bit of the binary number is a 0.

A Boolean function can be expressed as a —————— or ————————.

sum of minterms, product of maxterms

How do we convert from one canonical form to another?

In order to convert from one canonical form to another, interchange the symbols Σ and Π and list those numbers missing from the original form.

What does the logic diagram for sum-of-products consist of?

It consists of a group of AND gates followed by a single OR gate.

What does the logic diagram for product-of-sums consist of?

It consists of a group of OR gates followed by a single AND gate.

Sum-of-products and product-of-sums are called ——————.

standard forms

What do standard forms result in?

Standard forms result in a two-level structure of gates.

What’s the use of a buffer?

A buffer produces the transfer function without producing a logical operation and is used for power amplification of the signal.

What is gate-level minimization?

It’s the design task of finding an optimal gate-level implementation of the Boolean functions describing a digital circuit.

What does the map method do?

It provides a simple, straightforward procedure for minimizing Boolean functions and it’s regarded as a pictorial form of a truth table.

What is a K-map?

A K-map is a graphical tool used in digital logic design to simplify Boolean expressions. It helps identify patterns and groupings of 1's in a truth table, which can be used to derive the minimal Boolean expression. K-maps are commonly used for simplifying logic circuits and reducing the number of gates required.

The minterms are arranged in a sequence similar to the ————, where only one bit changes in value from one adjacent column to the next and from one adjacent row to the next.

Gray Code