Which arithmetic operation is common to binary, decimal, and hexadecimal number systems?

Which arithmetic operation is common to binary, decimal, and hexadecimal number systems?

• A. Addition
• B. Subtraction only
• C. Multiplication only
• D. Division only

Answer: (A)

All number systems share the same basic idea for adding numbers: align the digits by place value, add each column, and if the sum reaches or exceeds the base, carry to the next higher place. This carrying rule works the same way in binary (base 2), decimal (base 10), and hexadecimal (base 16). For example, binary addition carries when sums exceed 1, decimal addition carries when sums reach 10, and hexadecimal addition carries when sums reach 16. A simple hex example is 0x9 + 0x7 = 0x10, where the 1 is carried to the next position. This fundamental, base-spanning mechanism makes addition the clear example of a common arithmetic operation across these systems. While subtraction, multiplication, and division also exist in all bases, the question highlights addition because it best illustrates the universal carry-based process that applies in any base.

All number systems share the same basic idea for adding numbers: align the digits by place value, add each column, and if the sum reaches or exceeds the base, carry to the next higher place. This carrying rule works the same way in binary (base 2), decimal (base 10), and hexadecimal (base 16). For example, binary addition carries when sums exceed 1, decimal addition carries when sums reach 10, and hexadecimal addition carries when sums reach 16. A simple hex example is 0x9 + 0x7 = 0x10, where the 1 is carried to the next position. This fundamental, base-spanning mechanism makes addition the clear example of a common arithmetic operation across these systems. While subtraction, multiplication, and division also exist in all bases, the question highlights addition because it best illustrates the universal carry-based process that applies in any base.