1. BINARY Toby Wilson

2. LEARNING OBJECTIVES  Be able to convert binary to denary  Be able to convert denary into binary  Be able to explain how computers use binary

3. WHAT IS BINARY?  A number system that uses two digits, 0 and 1  (Base 2 = 0 & 1)  (Base 10 = 0,1,2,3,4,5,6,7,8 & 9)

4. A BIT  A bit is a digit in a binary number  It can be either 1 or 0

5. BINARY NUMBERS 0001  The number above includes 4 bits  Each bit is worth a different value  They work from right to left  In the number, 0 = 8 0 = 4 0 = 2 1 = 1

6. BINARY TO DENARY CONVERSION  Denary is a regular number. Eg 8  To convert a binary number into denary, you add up the value of each bit and there you have your result  1011 = 11 1011 8 0 1 2

7. QUESTION ANSWERS  1010 = 10  0011 = 3  1001 = 9  1111 = 15  10010 = 18  10111011 = 187

8. DENARY TO BINARY CONVERSION  This is the opposite of binary to denary  This is where you are given a denary number and you need to convert it in to binary  Eg. 22  22 – 16 (10000) = 6 6 – 4 (10100) = 2 – 2 (10110) = 0  22 = 10110

9. QUESTION ANSWERS  13 – 8 = 5 – 4 = 1 – 1 = 0 (1101)  7 – 4 = 3 -2 = 1 – 1 = 0 (111)  29 – 16 = 13 – 8 = 5 – 4 = 1 -1 = 0 (11101)  42 – 32 = 10 -8 = 2 -2 = 0 (10101)  62 – 32 = 30 – 16 = 14 – 8 = 6 – 4 = 2 – 2 = 0 (111110)  200 – 128 = 72 – 64 = 8 – 8 = 0 (11001000)

10. DEFINITIONS  Bit – Binary Digit  Nibble – 4 Bit Binary Number  Byte – 8 Bit Binary Number  Kilobyte – 10 Bit Binary Number  Megabyte – 20 Bit Binary Number  Gigabyte – 30 Bit Binary Number  Terabyte – 40 Bit Binary Number

11. HOW IS BINARY USED?  Binary is used to represent all types of data in a computer  For example, Colours  Colours are made up of Red, Green and Blue  Each of these colours are a byte  The combination of these three bytes will give you a huge range of colours to choose from

12. RESEARCH TASK  I need to find out how binary represents the following three areas:  Images  Sound  Text

13. HOW BINARY IS USED TO REPRESENT IMAGES  The pictures are made up of pixels, each with an 8-bit number representing a certain shade (Out of 256)

14. HEXADECIMAL DenaryBinaryHexDenaryBinaryHex 000000101010A 100011111011B 200102121100C 300113131101D 401004141110E 501015151111F 601106--- 701117--- 810008--- 910019--- 4C = 01001100 F5 = 11110101

15. HEXADECIMAL QUESTIONS DenBinHex 450010 110145 0010 110145

16. HOW TO ADD IT UP 70(16) = 0111 0000 = 112 70(10) = 0100 0110 = 46 To Binary: (128 64 32 16 8421) 0 0 0 0 0000 Then add all together To Hexidecimal: (8421 8421)Every 4 bits = 1 Digit 0000 0000 EG: 1101 1011 = 8 + 7 = 15