Hexadecimal Conversions 2.6 – Representing Data

What is Hexadecimal? Hexadecimal is a base 16 number system: there are 16 digits, 0 to 15. As we have only 10 single digits (0-9), we use upper-case letters A to F for the remaining digits. Therefore, hexadecimal digits are represented as: 0123456789ABCDEF

Why do we need Hexadecimal? We need hexadecimal numbers because of our human limitations. Computers do not use or understand hexadecimal, only binary. Hexadecimal is used because we get confused with large binary numbers, so we simplify them by representing them in hexadecimal notation. If we tried to give our phone number to someone in binary, it would be really difficult, therefore humans need an easier method. Since a byte is 8-bits, it makes sense to divide that binary number into two 4-bit numbers. Since 4-bits gives you a possible range of 0-15, a Base 16 system is easier to work with. Lets look at an example…

Hexadecimal Number system Denary 1 2 3 4 5 6 7 8 9 A 10 B 11 C 12 D 13 E 14 F 15 Remember that in denary (Base 10) we only have 10 single digits available to us… therefore, for Base 16 we use this representation.

Hex Denary 1 2 3 4 5 6 7 8 9 A 10 B 11 C 12 D 13 E 14 F 15 Hexadecimal Here is a byte (8-bits): Saying that is quite a mouthful, so its easier represented as hexadecimal. To convert the binary to hexadecimal the byte is split into two halves of 4 bits each. These are called nibbles. Each nibble is now converted into its denary number. Here are the nibbles with their place values. The denary numbers are 13 and 3. Therefore the hexadecimal representation is D3. It is far easier to remember D3 than 11010011. 1 1 1 8 4 2 1 8 4 2 1

Lets have a go… 1000 0111 0111 0101 0001 1000 0110 1110 1001 1111 1011 1011 0110 0110

Answers… 1000 0111 87 0111 0101 75 0001 1000 18 0110 1110 6E 1001 1111 9F 1011 1011 BB 0110 0110 66

Converting denary to hexadecimal 1 2 3 4 5 6 7 8 9 A 10 B 11 C 12 D 13 E 14 F 15 Here is denary number 213. To convert to hexadecimal, we must progressively divide by 16 until the result is 0 and remember the remainders. 213 ÷ 16 = 13 (remainder 5) 13 = D 5 = 5 D5

Lets have a go… 226 98 13 57 198 207 136

Answers… 226 E2 98 62 13 D 57 39 198 C6 207 CF 136 88