1 Learn what binary and denary mean 1

1. Learn what binary and denary mean. 1. Be able to convert numbers between binary and denary. 1. Understand the how 4 -bit binary works. 1

How do computers see the world? 2

A computer doesn’t think like a person can - it needs it’s own language! As a computer is a mathematical machine it uses a number system… First we need to understand what denary means. Denary means TEN. Humans have TEN fingers… the denary number system uses TEN numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9…. All other numbers are made up of these numbers. 3

In denary 9 lots of 10 is 90. . . so 8 lots of 10 plus 6 is 86. . . and 7 lots of 100 plus 2 lots of 10 plu 5 is 725. . . What would the following numbers be? 2 lots of 10 + 6____ of 10_____ 6 lots of 100 + 4 lots 3 lots of ten + 9____ of 10 + 7____ 9 lots of 100 + 6 lots 4 lots of 100 + 5 lots of 10 + 2____ 6 lots of 100 + 7 lots of 10 + 4

A computer on the other hand. . . Is a machine so it uses only TWO things - electrical signals that are either ON or OFF. How can we convert this to a language then? Simple- we use 1 for on and 0 for off! This is how your computer stores ALL data - images, videos, games, words and numbers! All stored as millions of 1’s and 0’s!! This is called BINARY because binary means TWO. 5

Each of these 1’s and 0’s is called a BIT. Heard the phrase 32 -bit or 64 -bit? But we are going to start off with a simple 4 -bit system to convert denary numbers into binary ones! BINARY is what we call BASE 2: It’s based on 2 numbers… so what would we call denary? ____ Our binary 4 bits are all multiplied by 2. This means we start with ONE (x 2) then TWO (x 2) then FOUR (x 2) then 8. What would the next two numbers be if we were using a 6 -bit system? ____ 6

These numbers are our “placeholders”. They are values we can add together! 8 4 2 1 The numbers in the white boxes tell us which numbers to use (think of 1 which is ON as YES and 0 which is OFF as NO!) 0 0 0 1 So this number is ONE because it is one lot of 1. 0 0 1 0 So this number is 2 because it is one lot of 2. 0 0 1 1 However this number is 3 because one lot of 1 + one lot of 2 =3 7

Quick Quiz: 1. Name three different types of data a computer stores: a. _____ b. _____ c. _____ 2. Binary is a way the computer reads but not stores data. TRUE / FALSE 3. Binary use electrical signals. TRUE / FALSE 4. Binary uses 1’s and 0’s to represent data? TRUE / FALSE 5. What is 12 in binary? _ _ 8