number base

2. Starter
• Think about it

3. Objectives
• Describe Number Bases
• Convert from base 2 to base 10
• Convert from base 10 to other
bases

4. • If DOVE = 415225,
What is: BROWN =
Hint: Decode the pattern

5. ANSWER
BROWN = 218152314
We make use of:
A B C D E F G H I J
1 2 3 4 5 6 7 8 9 10
K L M N O P Q R S T
11 12 13 14 15 16 17 18 19 20
U V W X Y Z
21 22 23 24 25 26

6. BRAIN STORM
• If DOVE = 46,
What is: BROWN =

7. Answer
• BROWN = 72

8. What are number bases?
They are simply a
system or way of
writing numbers

9. The same number written in
different form
Base 10 Base 2 Base 3 Base 4
45 101101 1200 231

10. Types of number bases
Number bases digit
Base 2 0,1
Base 3 0,1,2
Base 4 0,1,2,3
Base 5 0,1,2,3,4
Base 6 0,1,2,,3,4,5
Base 7 0,1,2,3,4,5,6
Base 8 0,1,2,3,4,5,6,7
Base 9 0,1,2,3,4,5,6,7,8
Base 10 0,1,2,3,4,5,6,7,8,9

11. Comparing number in base 10
and base 2
Base 10 Base 2
1 1
2 10
3 11
4 100
5 101

12. If you are to write 72 in
binary, will you have to start
from one to 72?
•No, you simply learn
the conversion from
base 10 to base 2

14. Try this
•What is 17 in base 2?
•Answer 10001

15. Converting from binary to denary
• Q.1: Convert the binary number 1001
to a decimal number.
• Solution: Given, binary number = 10012
• Hence, using the binary to decimal
conversion formula, we have:
• 10012 = (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1
× 2⁰)
• = 8 + 0 + 0 + 1
• = (9)₁₀

16. Try this
•Convert 11010012 into
an equivalent decimal
number.

17. Solution
• (1101001)₂ = (1 × 2⁶) + (1 × 2⁵) + (0 × 2⁴)
+ (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰)
= 64 + 32 + 0 + 8 + 0 + 0 + 1
= (105)₁₀