# Lesson 5 – Denary to Binary

Learning Objectives

• Understand that computers are digital devices so they use the binary number system
• Be able to convert a denary number to a binary 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 denary numbers to binary 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 denary numbers to binary numbers. (Level 5)

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

Keywords

Words to learn: binary, denary, convert, base

Starter

In the previous lesson we turned a binary (base 2) number, that computers use, into a denary (base 10) number, that we use.  In this lesson we will do the opposite – we will turn a denary (base 10) number into a binary number (base 2).

Main

To convert a number from denary to binary, take a denary number – I will use 91 in this example.

What we do is we keep dividing by 2, and we will keep track of any remainders.  Let me show you:

91 divided by 2 is 45 remainder 1
45 divided by 2 is 22 remainder 1
22 divided by 2 is 11 remainder 0
11 divided by 2 is 5 remainder 1
5 divided by 2 is 2 remainder 1
2 divided by 2 is 1 remainder 0
1 divided by 2 is 0 remainder 1

So we read the remainders backwards to get the binary number 1011011.  You’ve probably noticed this binary number has only seven digits – if you want to show it as a byte simply add some leading zeros, so as a byte the number is 01011011.  This technique is known as two’s compliment.

Get it?  Good – print out and try this worksheet which gives you a few to try out – remember to show your working!  Put the answers into your folder once you are finished.

Plenary

Once you’ve finished those exercises, have a go at this challenge. You’ll need to click the green flag, then use “full screen mode” (the little icon at the top left of the game). Each switch is a column (power of 2).  Flick the switches on in the correct order to make the numbers the robot asks for.  If you think that’s two easy, turn the timer on!  You can switch the program so it tests you on binary to denary conversion.

Still think that’s too easy?  Have a go at the Cisco Binary Challenge – you either have to convert binary to denary or denary to binary.  Good luck!