Overview Of Number Bases - SS3 ICT Past Questions and Answers - page 2

A number base, also known as a numeral system or radix, is a mathematical system used to represent numbers using a set of symbols. It affects the representation of numbers by determining how the value of each digit in a number is weighted. The base of a number system represents the number of unique symbols (digits) used in that system. For example, in the decimal system (base-10), we use 10 digits (0-9), and each digit represents a power of 10. In the binary system (base-2), we use 2 digits (0 and 1), and each digit represents a power of 2. Different bases offer different ways to express the same quantity, which can be more convenient for specific applications.

To convert the octal number 36 to decimal, we use the following formula:

(3 * 8^1) + (6 * 8^0) = (3 * 8) + (6 * 1) = 24 + 6 = 30

So, the octal number 36 is equivalent to the decimal number 30.

To convert a hexadecimal number to binary, you can replace each hexadecimal digit with its binary equivalent. Here's an example:

Hexadecimal: A3B

Binary equivalent:

A (hex) = 1010 (binary)

3 (hex) = 0011 (binary)

B (hex) = 1011 (binary)

So, A3B in hexadecimal is equivalent to 101000111011 in binary.

The digit position in different number bases represents the "place value" of each digit. In the decimal system, for example, the rightmost digit represents ones, the next digit to the left represents tens, the next hundreds, and so on. Similarly, in any base, each digit's position corresponds to a power of the base. Understanding the digit position is crucial for performing arithmetic operations, conversions, and understanding the magnitude of numbers in that base.

The binary number system is commonly used in computer science and digital electronics because it aligns perfectly with the binary nature of digital electronic circuits. In binary, data can be represented as a sequence of 0s and 1s, which corresponds well to the "on" and "off" states of electronic switches (transistors). Binary operations are straightforward to implement electronically, making it efficient for computers to process information. It also simplifies digital storage and communication, as each binary digit is easy to distinguish.