1. Hexadecimal
Dk Izzati Pg Haji Ahmad

2. Hex
Hexadecimal (also base 16, or hex) is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F (or alternatively a through f) to represent values For example, the hexadecimal number 2AF3 is equal, in decimal, to
(2 × 163) + (10 × 162) + (15 × 161) + (3 × 160) , or 10,995.
Each hexadecimal digit represents four binary digits, and the primary use of hexadecimal notation is as a human-friendly representation of binary coded values in computing and digital electronics. For example, byte values can range from 0 to 255 (decimal) but may be more conveniently represented as two hexadecimal digits in the range 00 through FF.

3. Conversion of binary to hex
Given a binary number, in order to convert it to a hex number, first of all, split the binary number into groups of 4 bits starting from the right.
Example: ₂
Hence, ₂ = 9B₁₆ 9 B

4. = (2 x 16³) + (10 x 16²) + (15 x 16¹) + (3 x 16⁰)
Conversion of hex to decimal
To convert hex to decimal, there are more than 1 alternative but the easiest way is to multiply each figure of the hex digit with 16ⁿ starting with the power of 0 (starts from the rightmost). Confusing? Let’s take a look at the example below:
Example: Given a hex number 2AF3, convert it to a decimal.
2AF3
= (2 x 16³) + (10 x 16²) + (15 x 16¹) + (3 x 16⁰) =
= 10,995
The power of 16 should start from 0 and not 1 and it should begin from the rightmost of the hex number.
The hex digit represented by an alphabet should be expand to a decimal number

5. How about the conversion of decimal to hex?
Let’s take a look at the table below.
Example 1:
Decimal Numberc
Operation
Quotient
Remainder
Hexadecimal Result
1792
112 7
÷ 16 =
DONE. 00
700

6. Example 2: 48879 3054 190 11 ÷ 16 = Done. 15 14 F EF EEF BEEF
      
Example 2:
Decimal Number
Operation
Quotient
Remainder
 Hexadecimal Result
48879
3054
190 11
÷ 16 =
Done. 15 14 F EF
EEF
BEEF

7. Conversion of hex to octal
To convert a hexadecimal number to an octal number, the first thing to do is to convert the hex number into something which is common between the two numeral system: BINARY. Each hex digit is represented by 4-bits binary
E.g.: Convert AF6D to an octal.
A = 10 = 1010
F = 15 = 1111
6 = 0110
D = 13 = 1101
Hence, AF6D =
An octal number is represented by 3-bits binary. Hence, starting from the right most side, divide the number above (hex converted to binary) into 3-bits binary. 

8. Hence, the answer for the conversion of AF6D to octal is 1275558
Divide the binary every 3-bits starting from right to left
ADD 0 to the last set if it is not exactly 3-bits
Change each set of
3-bits into decimal

9. Exercise 1. Convert the following binary numbers to hexadecimal a
Exercise 1. Convert the following binary numbers to hexadecimal a b c d e f g h

10. 2. Convert the following hexadecimal numbers to binary:
ADEA AF
C-9F-F2-A9 E
ABCDEF
F0E1D2C3B4A59687
B0C
1000

11. 3. Convert the following hexadecimal numbers to decimal:
a. AA
b. 123F
c. FEDCBA
d. D0-BE-D0
e. B8C
f. FF-FF-FF-FA
g. 10
h. FABE

12. 4. Convert the following decimal numbers to hexadecimal:9 32 73
255
1,025
4,099
65536
1,048,575