Binary Numbers (Base 2 Numbers): Addition,Subtraction, Multiplication and Division

• Addition in base 2
• Subtraction in base 2
• Multiplication & Division in base 2

ADDITION IN BASE TWO

We can add binary numbers in the same way as we separate with ordinary base 10 numbers.

The identities to remember are:-

0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10, 1 + 1 + 1 = 11, 1 + 1 + 1 + 1 = 100

SUBTRACTION IN BASE TWO

The identities to remember on subtraction are: 0 – 0 = 0, 1 – 0 = 1, 10 – 1 = 1, 11 – 1 = 10, 100 – 1 = 11

MULTIPLICATION AND DIVISION IN BASE TWO

In multiplication, 0 x 0 = 0, 1 x 0 = 0, 1 x 1 = 1.

When there is long multiplication of binary numbers, the principle of addition can be used to derive the answer. Under division, the principle of subtraction can be used.

READING ASSIGNMENT

Essential Mathematics for SS 1 pages 54 – 55

WEEKEND ASSIGNMENT

1.         Express 342₆ as a number in base 10.             (a) 342      (b) 3420       (c) 134

2.         Change the number 10010 to base 10             (a) 18       (b) 34           (c) 40

3.         Express in base two the square of 11               (a) 1001   (b) 1010       (c)  1011

4.         Find the value of (101)² in base two                (a) 1010   (b) 1111       (c)  1001

5.         Multiply 100001₂ by 11                        (a) 1001   (b) 1100011 (c)  10111

THEORY

1. Convert the following to binary number 10_ten(10_ten)²
2. Calculate 110₂ x (1011₂ + 1001₂ – 101₂)
3. Multiply 34₅ by 22₅.