Microcontroller numbering system

1. what is the numbering system:
are systems that are used to express numbers in various forms and are understood by
computers
types of numbering system :
Decimal
Binary
Hexadecimal
Octal

2. base of systems:
base :is defined as a set of digits used to represent
numbers
base of decimal : 10 (0-9)
base of binary : 2 (0,1)
base of hexadecimal : 16 (0-15)
base of octal : 8 (0-7)

4. 1-1 conversion from decimal to binary
○ Divide the decimal number to be converted by the
value of the binary base (2)
○ Get the remainder from Step 1
○ repeat step 2 until number becomes zero
○ the result will be the reminder from bottom to up

5. Number Operation result reminder
10 10/2 5 0
5 5/2 2 1
2 2/2 1 0
1 1/2 0 1
The binary number is : (1010)2

6. 1-2 conversion from decimal to hexadecimal
○ Divide the decimal number to be converted by the
value of the binary base (2)
○ Get the remainder from Step 1
○ repeat step 2 until number becomes zero
○ the result will be the reminder from bottom to up

7. Number Operation result reminder
20/16 20/16 1 4
1/16 1/16 0 1
The hexadecimal number is : (14)16

8. 2-1 : conversion from binary to decimal
1-List out the powers of 2 for all the digits starting
from the rightmost position.
The first power would be 20 and as we move on it
will be 21, 22, 23, 24, 25
2- Now multiply each digit in the binary number
starting from the right
3- add all the result of multiplication to each other

9. Example 2-1: convert (1010)2 to decimal
1 0 1 0
23 22 21 20
8 + 0 + 2 + 0 = 10

10. 1-the first is by converting the binary to a
decimal number
2-then converting a decimal number to a
hexadecimal number

11. Example 2-2: convert (11111010)2 to hexadecimal
2-2-1-by converting binary to decimal
1 1 1 1 1 0 1 0
27 26 25 24 23 22 21 20
128 + 64 + 32 + 16 + 8 + 0 + 2 + 0 = 250

12. 2-2-2-by converting decimal to hexadecimal
Number Operation Result Reminder
250 250/16 15 10
15 15/16 0 15
The hexadecimal number is (F A)

13. 3-1 conversion from hexadecimal to decimal
1-List out the powers of 16 for all the digits starting
from the rightmost position.
The first power would be 160 and as we move on it
will be 161, 162, 163, 164, …
2- Now multiply each digit in the binary number
starting from the right
3- add all the result of multiplication to each other

14. Example 3-1:convert (𝐴𝐴)16 to Decimal
15 10
161 160
240 + 10 = 250

15. 3-2 conversion from hexadecimal to binary
1-the first is by converting the hexadecimal to a
decimal number
2-then converting a decimal number to a binary
number

16. Example 3-2 :convert (𝐴𝐴)16 to binary
3-2-1: converting from hexadecimal to decimal
(See one of the previous slides)

17. 3-2-2: converting from (250)10decimal to binary
Number Operation Result reminder
250 250/2 125 0
125 125/2 62 1
62 62/2 31 0
31 31/2 15 1
15 15/2 7 1
7 7/2 3 1
3 3/2 1 1
1 1/2 0 1
The binary number is (11111010)2