Subtraction in bases involves performing arithmetic subtraction in number systems other than base 10, such as binary (base 2), octal (base 8), or hexadecimal (base 16). It requires understanding how to borrow and subtract digits within those specific bases.
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In base-n subtraction, if a digit being subtracted is larger than the digit it is being subtracted from, borrowing from the next higher place value is required.
Binary subtraction follows similar rules to decimal subtraction but only uses digits 0 and 1.
When borrowing in binary subtraction, you borrow a '2' instead of a '10' as in decimal subtraction.
In hexadecimal subtraction, digits range from 0 to F (where A=10 to F=15) and borrowing follows similar principles but within the base-16 system.
Understanding the concept of place value is crucial for performing accurate subtractions in any base system.
Review Questions
What happens when you need to subtract a larger digit from a smaller digit in base-n?
How do you handle borrowing in binary subtraction?
What are the digits used in hexadecimal numbers?
Related terms
Base Conversion: The process of changing a number from one base to another.
Binary Addition: The arithmetic operation of adding two binary numbers.
Hexadecimal System: A base-16 number system using digits 0-9 and letters A-F.