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conversion (binary, hex, denary) flashcards
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- 1In common denary system we all use, there are 9 different symbols. These are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We use these symbols to write numbers, so 573 means 5 lots of 100 7 lots of 10 and 3 lots of 1.However, in binary (base 2) we only have two different number values true (1) or false (0), which is where the system gets its name from, as it only has two values.
128 64 32 16 8 4 2 1 - 2In Binary, we have this table to represent our data in. There are only 8 digits in a binary number, which all correspond with values in the table. For example, this number 255 would be 11111111 in binary, as it equal to 1+2+4+8+16+32+64+128.To convert binary to denary (this is the easiest part), we first have to draw out this table:
128 64 32 16 8 4 2 1 - 3Then we have to fill in our values into the table. For example lets convert the binary number 10101010 into denary.We should start by drawing out and filling the table, so that it looks something like this:
128 64 32 16 8 4 2 1
1 0 1 0 1 0 1 0 - 4Now, we need to do some maths, namely 128+32+8+2, which will give us our answer to this questionwhich is 170.
- 5We start, as we would in any converting question, by drawing out our table, but this time with a change, as we need to fill it out with our number that we are converting at the top left going down, which in this case will be 187.187 / 2 = 108 remainder 1
108 / 2 = 54 remainder 0
54 / 2 = 27 remainder 0
27 / 2 = 13 remainder 1
13 / 2 = 6 remainder 1
6 / 2 = 3 remainder 0
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1 - 6This may appear quite complicated, but hey we need marks for working don’t we? We divide the denary number by two, noting down the remainder, which no one who can do basic maths has ever used since they were 8 years old.If you are like me, you can do it in your head, but make sure that you check the answer by converting your binary to denary after you have converted it.
- 7Part 2-Adding binary numbers This, is where the maths parts can become quite complicated if you do not memorise the basic rules for adding binary values together; these rules are: 0+0=0 0+1=1 1+1=10 1+1+1=11If you can successfully remember these rules, and are able to draw a table, you will be able to add binary, through this method.
To start with, you should create a table that looks something like this:
8 7 6 5 4 3 2 1
Number1
Number2
Working
answer - 8Decimal (Denary) Hexadecimal 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 A 11 B 12 C 13 D 14 E 15 FThe first part of this is a lot easier than you may think, as it is a relatively simple process to do when you get the hang of it.
Let’s convert the number 6F from hexadecimal into denary now. The first step would be for us to draw out the table shown below, as it makes the process a lot easier. - 9256 16 1 The next step would be to input the values into the table. Since we only have a two digit value, we only need to fill in two columns. 256 16 1 6 FNow we need to multiply these values, by doing 6 multiplied by 16 which is 96. The next step is to multiply 1 by F. This is not algebra, so we convert the f into its denary value of 15, which means we need to do 1x15, the result being 15. Then we need to add 96, and 15, giving us the final answer of 111.
So 6F=111. Now that wasn’t hard was it? - 10Now it’s time for the other way round: We first need to look at the size of the number we are converting to see whether it will have 1, 2, or 3 digits. A one digit number will have a one hexadecimal number, A denary number that is less than 256 (the largest byte value) will have two digits and any number bigger than 255 will have a three digit hexadecimal value.Let’s find the hexadecimal value of 94. 94 is lower than 255, so we know the hexadecimal value will only have 2 digits.
The next thing to do is to divide 94 by 16, which is 5.875, but we only write the 5, as there are only whole numbers in hexadecimal. 16x5=80, so we have 14 left, which is In Hex E. - 11So in hexadecimal, 94 is 5E. This is a somewhat overcomplicated method, but it is worthwhile knowing how to do this.AND ALWAYS SHOW YOUR WORKING!
- 12Part 5-converting hexadecimal to binary Let’s start with the fact that each byte is composed of 2 nibbles of data, and each nibble is made up of 4 separate bits of data. When we convert hexadecimal numbers to binary, we work in separate nibbles of data. To transfer hexadecimal you need to know two things, the denary equivalents for the hexadecimal numbers, and the binary table, used by everyone earlier in the topic, however we only require half of the table, so it looks something like this: 8 4 2 1We do this because each hex character is 1 nibble of data, so it will only ever have 4 bits in it.
As an example, let’s convert F6 from hex, into binary. The first step would be for us to set out the table below:
8 4 2 1 - 13Then we need to work out the denary values of F, and 6. The denary value for F is fifteen, so we need to use the numbers in the table to make fifteen: 8 4 2 1 1 1 1 1 Then we need to the exact same thing with 6. Luckily for us, 6 in hex is 6 in decimal, so we don’t need to spend much time converting it from hex to decimal. Now we draw out the table again, and fill in the details:8 4 2 1
0 1 1 0
The next step is to combine these two nibbles together, so we get the answer:
F6=11110110
That wasn’t hard now was it?
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- GCSE Computing Fichas sobre conversion (binary, hex, denary) flashcards, creado por Woollinwarriro el 08/12/2015.
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