## Representing and manipulating data in computers

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Introduction We know that a digit's worth depends on what position it is in relative to the other digits in the number.

How does the hexadecimal system work? The first thing to note is that there are 16 'numbers' in this system: It may well seem a little odd using letters to represent numbers: With a little practice, you will see what an excellent system this is.

Just to remind you, to show what binary to denary conversion is being used when you write down a number, it is common to use a subscript. As you know, when we write down numbers in our daily life, we omit the subscript because we assume that every one is using base Sometimes, especially in computer circles, binary to denary conversion is a dangerous assumption to make! If there is any doubt, binary to denary conversion add a subscript! When doing exam questions, always use a subscript, just to show how clever you are!

Let's convert a few hex numbers into denary. For the first few you do, you should write down the worth of each position. Then write the number you are converting underneath it. Finally, do the conversion. You have to think a little bit harder going the other way, from denary to hex.

But there is a great trick you can use - if you can use binary. Binary and hex are actually very closely related, much more so than first appears. Each hex digit is just a group of four bits!! As long as we can do binary to denary conversion off the top of our heads, there is a method for converting denary to hex binary to denary conversion also back again very quickly.

See if you can follow this example. We are going to online brokerage rankings globe and mail 10 into a hex number.

You should always check the hex answer you got. Of course, you could always check your answer using a calculator! This may seem a little long-winded to start with, but this method is very mechanical and always works.

Once you've done a few, you'll be an expert. Besides, it's good practice for binary conversion! Convert these numbers into their denary form: Convert these decimal numbers into hex: Why are nibbles important when using hex? Worth of each position.

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In our everyday lives we use a 'Denary' number system which has the number digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. You already know that computers can't work with our denary system, they need to use binary numbers to process data. When working with any number system, be it denary, binary or hexadecimal, the position of the number is important in order for you to be able to calculate its value.

The number on the far right, 3, is worth 3 units. The number to the left of 3, isn't worth 2, instead it is worth Now think about the number 1 in Again, this isn't worth the value of 1, and it hasn't been multiplied by 10 as the 2 was.

Because it is one position further to the left than 2, it is multiplied by , meaning it is worth The rule with base numbers is to multiply each digit on the left by a progressive factor of 10 in order to calculate its value. Likewise, when working with binary numbers, the position is important in order for you to be able to calculate the correct value.

For base-two binary numbers, you need to multiply each digit on the left by a progressive factor of 2. As with denary numbers, the calculations always work from right to left.

The number below has a 0 in the 32 position and the binary number in decimal is: Challenge see if you can find out one extra fact on this topic that we haven't already told you. This page is part of the old A specification - current syllabus here 2. Converting a denary number into a binary number Base 10 number system denary In our everyday lives we use a 'Denary' number system which has the number digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

This is called a 'base' number system. Here are some examples of denary numbers: Binary is a 'base-2' type of number which has only two digits, a 1 or a 0 Here are some examples of binary numbers: For example, with the denary system, think about the number So is arrived at by using the following calculation: Calculating binary numbers Likewise, when working with binary numbers, the position is important in order for you to be able to calculate the correct value.

The value 1 in binary represents the value one, the value 0 represents zero. Challenge see if you can find out one extra fact on this topic that we haven't already told you Click on this link: