Basic arithmetic in number bases - SS3 ICT Lesson Note

Number bases, also known as numeral systems, are methods of representing numbers using a specific set of symbols. The most common number base is the decimal system, which uses digits 0 through 9. However, there are various other bases used in mathematics and computing. Some important bases include:

Binary (Base 2): Uses only 0 and 1.

Octal (Base 8): Uses digits 0-7.

Decimal (Base 10): Our everyday base, using digits 0-9.

Hexadecimal (Base 16): Uses digits 0-9 and letters A-F to represent values 10-15.

Now, let's explore basic arithmetic operations in different bases:

 

Addition in Different Bases:

• Binary Addition: In binary, you add numbers much like in decimal. When you add 1 and 1, you get 10 (binary for 2). For example:

1102 (Binary) + 1112 (Binary) = 11012 (Binary)

1001 (Binary) + 1010 (Binary) = 10011 (Binary)

• Octal Addition: Octal addition is similar to binary or decimal addition, but it involves carrying over when the sum is greater than or equal to 8. For example:

45 (Octal) + 45 (Octal) = 100 (Octal)

77 (Octal) + 1 (Octal) = 100 (Octal)

 

Subtraction in Different Bases:

• Binary Subtraction: Subtraction in binary works much like decimal subtraction. When you subtract 1 from 0, you might need to borrow from a higher place value. For example:

11012 (Binary) - 1012 (Binary) = 10102 (Binary)

11012 (Binary) - 10012 (Binary) = 10002 (Binary)

• Octal Subtraction: Octal subtraction is similar, but it involves borrowing when necessary to ensure that the subtraction doesn't result in negative octal numbers. For example:

76 (Octal) - 23 (Octal) = 53 (Octal)

100 (Octal) - 1 (Octal) = 77 (Octal)

 

These are the basic principles of performing addition and subtraction in different number bases. The key is understanding the place values and carrying or borrowing when necessary, just as you do in the decimal system.