BASE NUMBERS

Base Numbers

Definition Of Base Numbers

The Base Number is the basis of each place value column in a number system.

More About Base Numbers

In a place value system, each column contains digits representing successive powers of the base number.
In a decimal system, the base number is 10.

Video Examples: Base Numbers

Examples of Base Numbers

The binary number 11001001₂ is equivalent to 20110
The binary number 110100₂ can be converted into decimal number as:
110100₂ = 1 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 0 × 20
= 32 + 16 + 0 + 4 + 0 + 0
= 52
So, the decimal equivalent of 110100₂ is equivalent to 52₁₀.

Solved Example on Base Numbers

Ques: Find the conversion of the decimal number 82 to base 6.

Choices:

A. 412 base 6
B. 142 base 6
C. 214 base 6
D. 224 base 6
Correct Answer: C

Solution:

Step 1: 82 divided by 6 leaves the remainder 4
Step 2: Again the quotient 13 divided by 6 leaves the remainder 1
Step 3: Once again, the quotient 2 divided by 6 leaves the remainder 2
Step 4: The answer is formed by taking the remainders in reverse order: 214 base 6.

Quick Summary

Base numbers define the structure of a number system.
In a base-n system, there are n unique digits (0 to n-1).
The decimal system (base 10) is the most commonly used system.
Other common base systems include binary (base 2), octal (base 8), and hexadecimal (base 16).

\[ N = d_n b^n + d_{n-1} b^{n-1} + ... + d_1 b^1 + d_0 b^0, where b is the base and d_i are the digits. \]

🍎 Teacher Insights

Use visual aids like blocks or counters to demonstrate different base systems. Emphasize the concept of place value and how it changes with different bases. Relate it to computer science and how binary numbers are fundamental.

🎓 Prerequisites

Place Value
Basic Arithmetic Operations
Exponents

Check Your Knowledge

Q1: What is the base number in the binary system?

A. 2 B. 8 C. 10 D. 16

Q2: What is the decimal equivalent of 110_2?

A. 3 B. 4 C. 6 D. 8

Frequently Asked Questions

Q: What is the significance of the base number?
A: The base number determines the number of digits available in the system and the weight of each place value column.

Q: How do you convert a number from one base to another?
A: Conversion involves successive division and remainders, or using place value expansion.