Find the sum and product of each of these pairs of numbers....

Find the sum and product of each of these pairs of numbers. Express your answers as a hexadecimal expansion. a) $(1 \mathrm{AE})_{16},(\mathrm{BBC})_{16}$ b) $(20 \mathrm{CBA})_{16},(\mathrm{A} 01)_{16}$ c) $(\mathrm{ABCDE})_{16},(1111)_{16}$ d) $(\mathrm{E} 0000 \mathrm{E})_{16},(\mathrm{BAAA})_{16}$

Find the sum and product of each of these pairs of numbers. Express your answers as a hexadecimal expansion.
a) $(1 \mathrm{AE})_{16},(\mathrm{BBC})_{16}$
b) $(20 \mathrm{CBA})_{16},(\mathrm{A} 01)_{16}$
c) $(\mathrm{ABCDE})_{16},(1111)_{16}$
d) $(\mathrm{E} 0000 \mathrm{E})_{16},(\mathrm{BAAA})_{16}$

Key Concepts

Arithmetic Operations in Different Bases

Performing arithmetic operations such as addition and multiplication in numeral systems other than base-10 involves applying the same principles as in decimal arithmetic, but with a different base and digit set. For hexadecimal arithmetic, this means carrying over or borrowing when sums or products exceed 15. Understanding these operations requires familiarity with the place-value system and the appropriate use of symbols (0–9 and A–F) for representing values.

Base Conversion Techniques

Base conversion techniques are important when working with non-decimal arithmetic because they allow numbers to be converted between different bases, such as from hexadecimal to decimal and vice versa. This is especially useful for verifying calculations and for understanding the magnitude of numbers represented in hexadecimal. Converting to and from hexadecimal often involves understanding powers of 16 and matching each digit to its corresponding power.

Hexadecimal Number System

The hexadecimal system is a base-16 numeral system that uses sixteen distinct symbols: 0–9 to represent values zero to nine, and A–F (or a–f) to represent values ten to fifteen. It is commonly used in computing and digital electronics because it provides a more human-friendly representation of binary-coded values, with each hexadecimal digit representing four binary digits (bits).

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