Topic 3: Data Hexadecimal

Hexadecimal We’ve looked at two number systems Denary (a.k.a. decimal): Base 10 Binary: Base 2 There are all kinds of number systems out there, but there’s one more useful one Called hexadecimal Data: Hexadecimal

Hexadecimal Hexadecimal is a base 16 number system First, let’s look at the values for a possible digit: 0-9 then A-F There’s a reason why we look at hexadecimal To do with its relation to binary Hexadecimal 1 2 3 4 5 6 7 8 9 A B C D E F Denary 10 11 12 13 14 15 Data: Hexadecimal

Hexadecimal Let’s look at the same values But this time we’ll include the binary values Notice how the denary value 15 fits into 4 binary bits, but 1 hexadecimal digit? Hexadecimal 1 2 3 4 5 6 7 8 9 A B C D E F Denary 10 11 12 13 14 15 Binary 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 Data: Hexadecimal

Hexadecimal This nice ‘coincidence’ makes representing binary easy 1 2 3 4 5 6 7 8 9 A B C D E F Denary 10 11 12 13 14 15 Binary 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 This nice ‘coincidence’ makes representing binary easy Instead of using 4 binary digits, we can use 1 hexadecimal digit It’s worth noting that this easier representation is purely for us Computers will still use binary Data: Hexadecimal

Converting to Hexadecimal As we have another number system, we’ll need to know how to convert From denary to hexadecimal From binary to hexadecimal From hexadecimal to denary From hexadecimal to binary Luckily, the best way to convert between hexadecimal and denary is to go through binary So we only need to work out how to go between hexadecimal and binary Denary Binary Hexadecimal Data: Hexadecimal

Converting to Hexadecimal Binary and hexadecimal neatly come together in a 1:4 ratio Converting binary to hexadecimal is easy We separate the binary number into groups of 4 Adding most-significant zero’s as needed Then translate each group into a hexadecimal digit Finally, we write those digits in order Example We have: 0110012 (2510) First we make the groups and add 0’s as needed 0001 1001 We get the denary value of each group (and get their hexadecimal value) 00012 = 110 = 116 10012 = 910 = 916 Then we write the digits in order 1916 Data: Hexadecimal

Convert the following denary values into hexadecimal 28 11 39 150 200 255 https://funtechacademies.co.uk/Academies/Timer/timer.html ANSWERS From top-left to bottom-right: 1C B 27 96 C8 FF Data: Hexadecimal

Converting from Hexadecimal Converting from hexadecimal to binary works in the exact opposite way We split the hexadecimal number into its digits We find the denary value of each digit We convert that denary value into a 4-bit binary number Finally, we write the binary numbers in order From left-to-right Example We have: A516 First we split the number into its digits (and convert each one into denary) A16 = 1010 516 = 510 Then we convert each number into 4-bit binary 1010 = 10102 510 = 01012 Then we write these numbers on after the other 101001012 Data: Hexadecimal

Convert the following denary values into hexadecimal B1 CD D7 https://funtechacademies.co.uk/Academies/Timer/timer.html ANSWERS From top-left to bottom-right: 242 161 140 177 205 215 Data: Hexadecimal

Some Uses of Hexadecimal There are two common uses of hexadecimal Colours Some systems use 1 byte per colour (red, green, and blue) Makes 24-bits in total Can be shortened to a 6-digit hexadecimal number Memory Addresses Come in 32-bit or 64-bit binary values Can be shortened to 8- or 16- digit hexadecimal numbers Useful Note In programming languages: 10: a denary value 1010 0x10: a hexadecimal value 1610 Data: Hexadecimal