# Lesson 4 – Binary to Denary

Learning Objectives

• Understand that computers are digital devices so they use the binary number system
• Be able to convert a binary number to a denary number

Learning Outcomes

All must know that computers are digital and this means that they have to use binary numbers to store information.  With lots of help, can convert a few binary numbers to denary numbers. (Level 4)

Most should know that computers are digital and be able to explain why therefore computers use binary numbers to store information.  With some help, can convert binary numbers to denary numbers. (Level 5)

Some could explain why computers use binary to store digital information and why binary is useful for computers.  Can confidently convert binary numbers to denary numbers and has completed all of the extension questions. (Level 6)

Keywords

Words to learn: binary, denary, convert, base

Starter

Watch this video which explains what binary (or base 2) is:

So as you can see from the video, computers use the binary (or base 2) number system whilst we as humans use the denary (or base 10) number system.

Binary has only two values 0 and 1
Denary has ten values 0,1,2,3,4,5,6,7,8,9

But why do computers use binary?  This video explains why:

Main

We are going to show you how to convert a binary number (base 2) into a denary number (base 10).  It’s easy if you follow the process below… First of all, we need to write out the powers of 2.  If you don’t know these, it’s easy:

Double of 1 = 2
Double of 2 = 4
Double of 4 = 8
Double of 8 = 16
Double of 16 = 32
Double of 32 = 64
Double of 64 = 128

So on a piece of paper, starting at the right hand side, you write out what you’ve worked out:

 128 64 32 16 8 4 2 1

Now we’re ready to tackle any binary number given to us!  Let’s try the number 01101010.  We write each binary digit underneath the powers of 2 we wrote:

 128 64 32 16 8 4 2 1 0 1 1 0 1 0 1 0

Where ever you see a 1, this means YES so you add the matching denary number – if there is a 0, this means NO so you ignore it.  So in the example above:

64+32+8+2 = 106

So 01101010 in binary = 106 in denary.

Get it?  Good – try these exercises : binrevex, making sure you show your working as well as your answers!

Once you have finished, make sure your name is clearly written at the top of your document and print it out for your folder.