Number Systems and Conversions

Which of the following is a base 8 number system?

What is the base of the decimal number system?

What advantage does the octal number system have over other systems?

In which number system does the digit '3' represent the same value as in the decimal system?

How do you convert the binary number (100111)2 into the decimal system?

What is the sum of the decimal equivalents when converting the binary number (100111)2?

Which digits are used in the hexadecimal number system?

Which statement about number systems is incorrect?

Number Systems

A number system represents numbers using digits or symbols consistently.
The digit's value depends on position and base.
Different number systems are used to represent numbers, the primary types are Binary, Decimal, Octal, and Hexadecimal.

Octal Number System

Uses digits 0 to 7 (base 8).
It's advantageous due to fewer digits compared to other systems like Binary, potentially reducing calculation errors.
Examples: 358, 9238, 14183588.

Decimal Number System

Uses digits 0 to 9 (base 10).
It's the system commonly used in daily life.
If a number has no specified base, it's assumed to be decimal (base 10).
Examples: 72310, 524710, 3210, 983710.

Conversion from Binary to Decimal

To convert a binary (base 2) number to decimal (base 10):
- Multiply each digit of the binary number, starting from the rightmost, with increasing powers of 2 (2^0, 2^1, 2^2, and so on).
- Add the results of these multiplications.
Example 1: Convert (100111)2 to decimal
- (1 x 2^5) + (0 x 2^4) + (0 x 2^3) + (1 x 2^2) + (1 x 2^1) + (1 x 2^0) = 32 + 0 + 0 + 4 + 2 + 1 = 39
Example 2: Convert (111111)2 to decimal
- (1 x 2^5) + (1 x 2^4) + (1 x 2^3) + (1 x 2^2) + (1 x 2^1) + (1 x 2^0) = 32 + 16 + 8 + 4 + 2 + 1 = 63

Explore the fundamentals of various number systems including Binary, Decimal, and Octal. This quiz covers the advantages of each system and guides you through conversions, especially from Binary to Decimal. Test your understanding of how different bases affect calculations and representations of numbers.