Each place value in a binary number represents $\qquad$ raised to the appropriate power.
A. 10
B. 2
C. 0
D. 1
Answer (2)
In binary numbers, each place value corresponds to a power of 2. Thus, the answer is 2. Understanding this is foundational in mathematics and computer science.
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Binary numbers are base-2 numbers.
Each place value in a binary number represents a power of 2.
Therefore, each place value is 2 raised to the appropriate power.
The answer is 2 .
Explanation
Understanding Binary Numbers The question asks us to identify the base that is raised to a power to represent each place value in a binary number. Let's analyze what binary numbers are and how their place values work.
Place Values in Binary Binary numbers are base-2 numbers. This means that each digit in a binary number can only be 0 or 1. Each place value in a binary number represents a power of 2. For example, the rightmost digit represents 2 0 , the next digit to the left represents 2 1 , then 2 2 , and so on.
Identifying the Base Therefore, each place value in a binary number represents 2 raised to the appropriate power.
Final Answer The correct answer is 2.
Examples
In computer science, binary numbers are used to represent all data and instructions. Each bit (binary digit) in a computer's memory can be either 0 or 1. These bits are grouped together to represent larger numbers, characters, and other data. Understanding binary place values is crucial for working with computer hardware and software. For example, an 8-bit byte can represent numbers from 0 to 2 8 − 1 = 255 .
