Binary, Octal and Hex Numbers Copyright Thaddeus Konar Introduction to Binary, Octal and Hexadecimal Numbers Part 1 – General Notation Thaddeus Konar 5/22/2019 Slide # 1 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

Binary, Octal and Hex Numbers Copyright Thaddeus Konar Decimal Integers 8934098798347298763287632 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. 09832198798237986498762380236409 If the world would be like Simpsons (and I am glad it is not) the natural notation would be octal (8 fingers) 9654327 4576 78543 8374567301 5/22/2019 Slide # 2 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

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 5/22/2019 Slide # 3 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

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) 5/22/2019 Slide # 4 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

Decimal Integers (Cont) What does 58345 ‘really’ mean: 58345 5 * 1 =5 4 * 10 =40 3 * 100 =300 8 * 1000 =8000 5 * 10000 =50000 =58345 5/22/2019 Slide # 5 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

Decimal Integers (cont) Lets look at the properties of the decimal integers: Base = 10 (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 5/22/2019 Slide # 6 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

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 5/22/2019 Slide # 7 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

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+40+800+7000 5/22/2019 Slide # 8 Binary, Octal and Hex Numbers Copyright Thaddeus Konar