Division in a base

Definition

Division in a base is the process of dividing numbers expressed in a specific numeral system, such as binary, octal, or hexadecimal. It follows similar principles to division in the decimal system but requires adjustments based on the base.

5 Must Know Facts For Your Next Test

1. Division in different bases requires understanding place values specific to that base.
2. In base systems like binary (base-2), each digit represents an increasing power of 2 starting from right to left.
3. To perform division accurately, you often need to convert the dividend and divisor to their decimal equivalents and then back to the original base.
4. The process involves repeated subtraction or long division adapted for the specific base system.
5. Remainders must be handled carefully, ensuring they are represented within the constraints of the given base.

Review Questions

• How do you handle remainders when performing division in a non-decimal base?
• What is the first step when dividing two numbers in a base-8 system?
• Why is it sometimes necessary to convert numbers into decimal form during division?

Related terms

Base System: A numeral system with a set number of distinct digits and a specific base value.

Binary Division: The process of dividing numbers specifically within the binary (base-2) numeral system.

Place Value: The numerical value that a digit has by virtue of its position in a number.