The binary system is most commonly used in modern computing as it directly corresponds to the on/off states of electronic circuits.

Hexadecimal is most efficient for representing large binary numbers in a compact form, as it condenses four binary digits into one hexadecimal digit.

The hexadecimal system is most efficient for representing large binary numbers due to its compactness.

The hexadecimal system is commonly used in programming to represent memory addresses due to its compactness.

The hexadecimal system is primarily used for color representation in web design, allowing for a compact representation of RGB values.

The binary numeral system is primarily used in digital electronics and computer science due to its simplicity and efficiency.

The binary system is primarily used in digital electronics due to its two-state nature.

The hexadecimal system uses digits 0-9 and letters A-F to represent values from 0 to 15.

The octal numeral system uses the digits 0-7.

The binary system is primarily used in computer science for data representation as it directly corresponds to the on/off states of electronic circuits.

The binary system is primarily used in digital electronics due to its two-state nature (0 and 1).

The passage captures digital sum as a practical tool that enhances various digital processes, highlighting its contemporary relevance.

The passage captures the essence that digital sum is foundational in modern computing, emphasizing its importance in various applications.

The base of a numeral system refers to the number of unique digits used in that system.

In a positional numeral system, the position of a digit determines its value, such as in decimal or binary systems.

The author expresses a supportive and optimistic view of digital sum, showcasing its benefits and potential.

The author presents digital sum in an enthusiastic manner, providing informative insights into its significance.

The conclusion emphasizes that digital sum is fundamental and has numerous applications across various domains.

The conclusion of the passage asserts that digital sum continues to be a fundamental concept in the field of technology.

3x ≡ 9 (mod 6) has no solution because 3 and 6 are not coprime, and 9 is not divisible by the gcd(3, 6).

8 ≡ 15 (mod 8) is false; the correct answer is 5 ≡ 10 (mod 5) is true.

All options are valid, but 5x ≡ 10 (mod 5) simplifies to 0 ≡ 0, which is trivially true.

Composite numbers are defined as natural numbers greater than 1 that are not prime, meaning they have more than two distinct positive divisors.

A common rule for checking divisibility by 7 is to double the last digit and subtract it from the rest of the number; if the result is divisible by 7, then the original number is also divisible by 7.

The decimal system is a base-10 system, which is widely used in everyday calculations.

The hexadecimal system is a base-16 system that includes the digits 0-9 and letters A-F.

For a number to be divisible by 11, the difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11.

The decimal number 10 is represented as 1010 in binary.

A number is divisible by 10 if it ends in 0.

For a number to be divisible by 11, the difference between the sum of the digits in odd positions and even positions must be divisible by 11.