1. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Introduction to Binary, Octal and Hexadecimal Numbers Part 2 – Binary Numbers
Thaddeus Konar
11/20/ Slide # 1
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

2. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Binary Integers 1
Just as the each digit (position) in decimal integer is represented by the power of 10, binary integers are numbers where each digit is represented by the power of 2 (Base = 2).
Digits range: 0 -> (Base - 1) Number of values represented by a single digit: Base
Digits range: 0 -> 1 (0,1) Number of values represented by a single digit : 2
11/20/ Slide # 2
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

3. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Binary Integers 2
In the decimal number the digits could be 0,1,2,3,4,5,6,7,8,9. (0 -> Base-1). As we can see the binary number digits could only be either 0 or 1 (0 ->Base-1).
The single decimal number can represent 10 values, and the single binary number can represent only 2 values.
11/20/ Slide # 3
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

4. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Binary Integers 3
Binary integer will be a combination of 1s and 0s.
Please recall the formula (and remember that now Base=2):
(D0*B0)+(D1*B1)+(D2*B2)+(D3*B3)+…(Dn*Bn)
B0=1, B1=2, B2=4, B3 =8, B4=16, B5=32, B6 =64…
Lets look at the binary number
D0=0, D1=1, D2=1, D3=1, D4=0, D5=1
11/20/ Slide # 4
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

5. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Binary Integers 4
… means: (0*20)+(1*21)+(1*22)+(1*23)+(0*24)+(1*25) = (0*1)+(1*2)+(1*4)+(1*8)+(0*16)+(1*32) = 4610
Here are the first few binary numbers:
00002 = 010
01002 = 410
10002 = 810
11002 = 1210
= 1610
00012 = 110
01012 = 510
10012 = 910
11012 = 1310
= 1710
00102 = 210
01102 = 610
10102 = 1010
11102 = 1410
= 1810
00112 = 310
01112 = 710
10112 = 1110
11112 = 1510
= 1910
11/20/ Slide # 5
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

6. Binary Conversion Example
Convert binary number to decimal:
10111
1 * 1 =1
1 * 2 =2
1 * 4 =4
0 * 8 =0
1 * 16
=16
=23
11/20/ Slide # 6
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

7. Convert binary number to decimal:
1 * 1 =1
0 * 2 =0
0 * 4 =0
1 * 8 =8
1 * 16
=16
1 * 32
=32
0 * 64 =0
1 * 128
=128
=185
11/20/ Slide # 7
Binary, Octal and Hex Numbers Copyright Thaddeus Konar