1. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Introduction to Binary, Octal and Hexadecimal Numbers Part 1 – General Notation
Thaddeus Konar
5/22/ Slide # 1
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

2. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Decimal Integers
There is nothing ‘unique’ about number 10, but because we have 10 fingers, the decimal notation (from Latin decem and Greek Deka: 10) seems ‘natural’ to us.
If the world would be like Simpsons (and I am glad it is not) the natural notation would be octal (8 fingers)
4576
78543
5/22/ Slide # 2
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

3. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Decimal Integers
Each digit (counting from the right) represents next power of ten, the rightmost digit represents 1s, next digit represents 10s, next 100s, and so on: …,10000, 1000, 100, 10, 1 which is the same as:
…,104 ,103, 102, 101, 100
(Please remember that any number X to zero (0) power equals 1!)
X0 = 1
5/22/ Slide # 3
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

4. Decimal Integers (cont)
7845 means: (5*1)+(4*10)+(8*100)+(7*1000)
and this is same as: (5*100)+(4*101)+(8*102)+(7*103)
5/22/ Slide # 4
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

5. Decimal Integers (Cont)
What does ‘really’ mean:
58345
5 * 1 =5
4 * 10
=40
3 * 100
=300
8 * 1000
=8000
5 * 10000
=50000
=58345
5/22/ Slide # 5
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

6. Decimal Integers (cont)
Lets look at the properties of the decimal integers:
Base = (1, 10, 100, …) (100, 101 , 102 , …)
Digits range: 0 -> 9 (0,1,2,3,4,5,6,7,8,9)
Number of possible values represented by single digit: 10
Please note that number of digits equals Base, and range goes from zero to (Base –1).
Digits range: 0 -> (Base - 1) Number of possible values represented by single digit: Base
5/22/ Slide # 6
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

7. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
General Notation
Any number is represented by combination of single digits Dx, where x is the position of the digit counting from the right. The value of Dx can be only the digits between (and including) 0 and (Base-1).
…D5D4D3D2D1D0
Using our example decimal number 7845
D0 =5, D1=4, D2=8, and D3 =7
5/22/ Slide # 7
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

8. General Notation (cont)
We can see that any number really means:
(D0*B0)+(D1*B1)+(D2*B2)+(D3*B3)+…(Dn*Bn)
In our example number 7845 (base 10) means: (5*100)+(4*101)+(8*102)+(7*103)=
5/22/ Slide # 8
Binary, Octal and Hex Numbers Copyright Thaddeus Konar