1. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Introduction to Binary, Octal and Hexadecimal Numbers Part 4 – Hexadecimal Numbers
Thaddeus Konar
11/11/ Slide # 1
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

2. Hexadecimal (Hex) Integers 1
Just as the each digit (position) in decimal integer is represented by the power of 10, in binary integer - power of 2, in octal numbers - power of 8, and in hex integers – power of 16 (Base = 16).
Digits range: 0 -> (Base - 1) Number of values represented by a single digit: Base
Digits range: 0 -> 15 (0,1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F) Number of values represented by a single digit: 16
11/11/ Slide # 2
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

3. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Hex Integers 2
In the decimal number the digits could be 0,1,2,3,4,5,6,7,8,9. (0 -> Base-1), in binary 0,1 (Base-1), in octal 0,1,2,3,4,5,6,7. (0 -> Base-1). In hex numbers the digits would be 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F (0 -> Base-1). The letters A through F represent the decimal numbers 10 to 15.
The single decimal number can represent 10 values, the single binary number can represent only 2 values, the single octal number can represent 8 values, and the single hex number can represent 16 values.
11/11/ Slide # 3
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

4. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Hex Integers 3
In Hex integers Base = 16.
Please recall the formula:
(D0*B0)+(D1*B1)+(D2*B2)+(D3*B3)+…(Dn*Bn)
B0=1, B1=16, B2=256, B3 =4096, B4=65536…
Lets look at the hex number A59C
D0=C, D1=9, D2=5, D3=A
11/11/ Slide # 4
Binary, Octal and Hex Numbers Copyright Thaddeus Konar

5. Binary, Octal and Hex Numbers Copyright Thaddeus Konar
Hex Integers 4
…A59C means: (12*160)+(9*161)+(5*162)+(A*163) = (12*1)+(9*16)+(5*256)+(10*4096) =
Here are the first few hex numbers:
00016 = 010
00416 = 410
00816 = 810
00C16 = 1210
01016 = 1610
00116 = 110
00516 = 510
00916 = 910
00D16 = 1310
01116 = 1710
00216 = 210
00616 = 610
00A16 = 1010
00E16 = 1410
01216 = 1810
00316 = 310
00716 = 710
00B16 = 1110
00F16 = 1510
01316 = 1910
11/11/ Slide # 5
Binary, Octal and Hex Numbers Copyright Thaddeus Konar