1. Number Systems

2. Decimal Numbers Decimal stands for 10
Decimal is the base 10 Number System
It has 10 unique symbols
The largest symbol is the base – 1
10 – 1 = 9
9 is the largest symbol in Decimal numbers

3. Decimal Numbers
units
4000
300 50
+ 6
435610

4. Decimal Numbers Weight origin 103 102 101 100 Weights 1000 100 10 1
Number MSD LSD
6000
300 60
+ 4
636410

5. Binary Numbers Binary stands for 2 Binary is the base 2 number system
It has two unique symbols
0 and 1
The largest symbol in Binary is the base – 1
2 – 1 = 1
1 is the largest symbol in the Binary Number system

6. Binary Numbers Weight origin 23 22 21 20 Weights 8 4 2 12
+ 1
1110

7. Counting in Binary
Weight decimal

8. Converting from Decimal to Binary
The decimal number 55 = ____ In binary
55 ÷ 2 = 27.5* 1 LSB
27 ÷ 2 =
13 ÷ 2 =
6 ÷ 2 =
3 ÷ 2 =
1 ÷ 2 = MSB
= 5510
* If the remainder is .5 place a 1 to the right. If 0 place 0 to right

9. Octal Number System Octal stands for Eight
Octal is the base 8 Number System
It has 8 unique symbols
The largest symbol is the base – 1
8 – 1 = 7
7 is the largest symbol in the Octal number system

10. Octal Number System Weight origin 83 82 81 80 Weights 512 64 8 1
1024 64 48
+ 7
114310

11. Hexadecimal Number System
Hex = 6 and Decimal = = 16
Hex is the base 16 Number System
It has 16 symbols
It must have 16 UNIQUE Symbols
A B C D E F
The largest symbol is 16 – 1 = 15 or F

12. Hexadecimal Number System
Weight origin
Weights
Number A F 16
4096
512
160
+ 15
478310

13. Octal Conversions The largest symbol in Octal is 7
It requires three binary bit to represent the number 7 
To convert a binary number to Octal, start with the LSB and mark off groups of 3.
LSB
Write Octal symbol below

14. Octal Conversions To convert an Octal number to binary:
Write the three bit binary equivalent below =
Leading zeros can be left off.

15. Convert Binary to Hex The largest symbol in Hex is 15 or F
It requires four binary bits to represent the number 15 or the symbol F  11112
To convert a binary number to Hex, start with the LSB and mark off groups of 4.
LSB
Write Hex symbols below
B A E 16

16. Convert Hex to Binary
To convert Hex to Binary, write the 4 bit Binary equivalent below each Hex digit.
A F 16 =