Untitled Quiz

<p>Both A and B (D)</p> Signup and view all the answers

<p>To enhance the hardware efficiency. (D)</p> Signup and view all the answers

<p>True or On (B)</p> Signup and view all the answers

<p>Automatic control through programming (A)</p> Signup and view all the answers

<p>First Generation (A)</p> Signup and view all the answers

<p>0 (B)</p> Signup and view all the answers

<p>AND (C)</p> Signup and view all the answers

<p>Transistors (C)</p> Signup and view all the answers

<p>Limited programming capabilities (D)</p> Signup and view all the answers

<p>Based on their usage or applications (A)</p> Signup and view all the answers

<p>They could only be programmed in machine language (B)</p> Signup and view all the answers

<p>Physical labor (A)</p> Signup and view all the answers

<p>1950s (C)</p> Signup and view all the answers

<p>Represent each premise with a symbol (D)</p> Signup and view all the answers

<p>Truth table method (D)</p> Signup and view all the answers

<p>Null Law (D)</p> Signup and view all the answers

<p>The complement of the OR of terms is equivalent to the AND of complements (C)</p> Signup and view all the answers

<p>A + BC (C)</p> Signup and view all the answers

<p>Distributive Law (D)</p> Signup and view all the answers

<p>Reduction of Boolean expressions (D)</p> Signup and view all the answers

<p>It simplifies to A (B)</p> Signup and view all the answers

<p>The result of both sum and product operations is in B. (B)</p> Signup and view all the answers

<p>a * 1 = a (C)</p> Signup and view all the answers

<p>The order of addition does not affect the sum. (A)</p> Signup and view all the answers

<p>The distribution of multiplication over addition. (D)</p> Signup and view all the answers

<p>a + a' = 1 (A)</p> Signup and view all the answers

<p>0 + 1 = 1 (A)</p> Signup and view all the answers

<p>The relationships defined by the axioms hold true. (C)</p> Signup and view all the answers

<p>It showcases how product of sums can be simplified. (A)</p> Signup and view all the answers

<p>NOT, AND, OR (D)</p> Signup and view all the answers

<p>An axiom can form its dual by changing OR to AND and vice versa. (C)</p> Signup and view all the answers

<p>X is raining, Y is bad weather. (C)</p> Signup and view all the answers

<p>False (C)</p> Signup and view all the answers

<p>AND (C)</p> Signup and view all the answers

<p>The output values based on input conditions. (B)</p> Signup and view all the answers

<p>Combination of AND operations. (D)</p> Signup and view all the answers

<p>True (C)</p> Signup and view all the answers

<p>B + CD (D)</p> Signup and view all the answers

<p>0 (D)</p> Signup and view all the answers

<p>Group 1 and Group 2 (A)</p> Signup and view all the answers

<p>B + CD (B)</p> Signup and view all the answers

<p>A=1, B=0, C=1 (B), A=0, B=0, C=0 (D)</p> Signup and view all the answers

<p>They can be mapped as though the map were bent (D)</p> Signup and view all the answers

<p>3 (B)</p> Signup and view all the answers

<p>0 (D)</p> Signup and view all the answers

Computers excel at repetitive tasks, long-term storage, automatic control, and programmability (flexible operations controlled by stored instructions).

A way to categorize computers based on their technological advancements throughout time.

Early computers (1940s-1950s) using vacuum tubes as components. Programmed in machine language.

Electronic components used in first-generation computers that generated heat and used significant electricity.

The ability of a computer to hold instructions for a task in memory, allowing it to run automatically.

The specific instructions used to program first-generation computers. Very low-level coding.

Computers using transistors instead of vacuum tubes. Improved on the first generation.

Electronic components in second-generation computers that replaced vacuum tubes, making computers smaller and more efficient.

A logical calculus used to describe and simplify logic circuits.

In Boolean algebra, the AND operator (represented by a dot) returns '1' only if both inputs are '1'.

In Boolean algebra, the OR operator (represented by +) returns '1' if at least one input is '1'.

Inverts the input. If input is '1', output is '0'. If input is '0', output is '1'.

Another name for Boolean algebra.

This consists of 0 (false/off), and 1 (true/on).

The numbers or logic values processed by the operators.

Electronic circuits that perform a Boolean operation.

A set of rules governing operations in Boolean algebra, defining properties like closure, identity, commutation, distribution, and inverse.

For any two elements in a Boolean algebra, the result of applying either OR (+) or AND (.) operation remains within the algebra.

The identity element for OR (+) is 0 (false), while for AND (.) it is 1 (true). Applying these to any element returns that element.

The order of elements doesn't matter when applying OR (+) or AND (.) operations.

Applying AND (.) over OR (+) or vice versa distributes the operation across the elements.

For every element in a Boolean algebra, there is an inverse element. ORing (+) an element with its inverse results in 1 (true), while ANDing (.) them yields 0 (false).

A table used to demonstrate the outcome of Boolean operations on different combinations of input values.

The process of checking if the proposed axioms hold true for all possible combinations of input values, often using a truth table.

In Boolean algebra, any theorem has a corresponding dual theorem formed by exchanging operators (AND with OR) and identity elements (0 with 1).

The order of operations in Boolean Algebra is NOT (highest), followed by AND, then OR. Brackets can be used to override this order.

A truth table shows the output (result) of a Boolean expression based on different combinations of input truth values (True or False).

A Boolean expression can represent real-life conditions like taking an umbrella based on it being rainy or the weather forecast being bad.

Another real-life example involves sweeping the class only if the windows are open and the class is empty. This translates to a Boolean expression with AND logic.

Variables in Boolean expressions represent propositions (statements) that can be either true or false.

In a Boolean expression, the output (Z) represents the result of the logic applied to the input variables (X and Y).

Boolean expressions are made up of variables (X, Y), logical operators (NOT, AND, OR), and parentheses to define the order of operations.

A statement that combines variables (representing inputs) and logical operators (AND, OR, NOT) to produce a true or false result.

Reducing complex Boolean expressions to their simplest form using Boolean algebra rules and techniques like Karnaugh maps.

A visual tool used to simplify Boolean expressions by grouping adjacent cells representing true values.

A set of rules that define how to invert complex Boolean expressions by complementing each term and changing the logic operator.

In a Karnaugh map, grouping adjacent 1s together to create larger groups, representing logical simplification.

After grouping 1s in a K-map, the final expression is formed by ORing (adding) the individual group results.

Using a Karnaugh map to simplify Boolean expressions by identifying groups of adjacent 1s and representing them with minimal terms.

Converting a truth table into a Karnaugh map to visualize the Boolean function and simplify it.

In a K-map, 1s that are next to each other, either horizontally or vertically, can be grouped together.

The size of a group in a K-map determines the corresponding term in the simplified expression, with larger groups leading to simpler terms.

A K-map can be visualized as bent or wrapped around so that cells on the edge are considered adjacent.

The final expression obtained after applying K-map simplification, representing the same logic with fewer terms.