Number systems are notations that represent numerals or numbers. The main number systems discussed are decimal, binary, octal, and hexadecimal. Decimal uses base 10 with digits 0-9. Binary uses base 2 with digits 0-1. Octal uses base 8 with digits 0-7. Hexadecimal uses base 16 with digits 0-9 and A-F and was introduced as an offshoot of octal to avoid deviations from binary. Each system was presented with example number representations.

1. NUMBER SYSTEMS

2. What is a
Number System?

3. NUMBER SYSTEMS
● are also called “Numeral System”.
● Is any notation that represents
numerals or numbers.

4. DECIMAL
● Decimal number system has a base
or radix of 10 numbers
● Are notated with one digit starting
from 1-9 and ending the sequence
with 0 prefixed with another digit.

5. Example of Decimal:
1 11 21 91 991 9991
2 12 22 92 992 9992
3 13 23 93 993 9993
4 14 24 94 994 9994
5 15 25 95 995 9995
6 16 26 96 996 9996
7 17 27 97 997 9997
8 18 28 98 998 9998
9 19 29 99 999 9999
10 20 30 100 1000 10000

6. BINARY
● Considered as the “computer machine
language”.
● The binary simulates the toggle switches
that a computer uses to perform its
calculation.

7. BINARY
● Has a base or radix of 2.
● In terms of counting, a digit is
added is sequence for every two
counts using only the symbols 0
and 1.

8. Example of Binary:
Binary Decimal
0 0
1 1
10 2
11 3
100 4
101 5
Binary Decimal
110 6
111 7
1000 8
1001 9
1010 10
1011 11
Binary Decimal
1100 12
1101 13
1110 14
1111 15
10000 16

9. OCTAL
● A result of simplifying the
representation of characters in
programming a computer.
● Programmers thought of grouping the
binary bits into 3 called “octets”.

10. OCTAL
● Thus, 2^3 is equal to 8 deriving
the name octal.
● The octal number system uses only
eight digits (0 to 7).

11. Example of Octal:
Octal Decimal
0 0
1 1
2 2
3 3
4 4
5 5
Octal Decimal
6 6
7 7
10 8
11 9
12 10
13 11
Octal Decimal
14 12
15 13
16 14
17 15
20 16

12. HEXADECIMAL
● is a spin off from octal system.
● Not having the option to deviate
from it’s binary root, hexadecimal was
introduced.
● Has a base or radix of 16.

13. Example of Hexadecimal:
Dec 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hex 0 1 2 3 4 5 6 7 8 9 A B C D E F
Dec 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Hex 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F