Topic 4 Base Jumping Objectives Convert from binary to denary Convert from denary to binary Use addition with binary Create and crack binary codes with ASCII Activity 4.1 Get Cracking! (convert binary to denary) In the following activities you will practise converting binary numbers to denary numbers, using binary placeholders, sounds, colours and text. Task A Starter for 10 The denary number system is also referred to as the decimal number system and is what humans use. Computers use a binary number system to process and store information. 1) To get started, try converting the binary numbers below to denary. 1001 0100 0001 0001 1100 0011 Task B Mind your Language Binary code can be represented as sound, e.g. on and off. Scenario: Interplanetary travel means that Blurb needs to communicate with other beings in a different language to his own. Blurb has been confronted by a peculiar-looking being from another planet who makes rude noises at him. Blurb is convinced that the alien is blowing raspberries at him until he begins to recognise a pattern and sequence in the language. Raspberry! Raspberry!? Raspberry Aid: a raspberry is a 1 and a blank square is 0
1) Use your knowledge of binary and the ASCII table to help Blurb crack the message from the alien. Task C Cracking Jokes Now that Blurb can understand the alien, he tries out a (bad) joke on him. 1) See if you can get the answer. What type of crazy bug lives on the moon? A 0100 1100 0111 0101 0110 1110 0110 0001 0111 0010 0111 0100 0110 1001 0110 0011 0110 1011!
Task D Optical Illusion Optical storage devices, such as CDs and DVDs, use on/off light to read data. 1) Decode the following tables. The dark squares represent off and the light squares represent on. Work out what the flashing light represents in binary and then find the ASCII code it represents.
Task E Mug Shots Binary code can be represented as images or colours (e.g. blank square or square containing image). Scenario Blurb has some passport photos of himself. Blurb lays out the photos with some face up, and some face down. 1) a) Work out the binary code from the pictures below face up represents 1 and face down represents 0 (remember 1 is on and 0 is off). b) Now convert the binary code to denary: c) Now encode the denary number using the ASCII table at the end of this topic. What ASCII character is Blurb displaying?
Task F Making Faces Bitmap images are made up of tiny squares or picture elements called pixels. Each pixel can be represented by a colour to make a picture. 1) What picture do you get when you convert the following code to colours? (Black on and white off) 0011 1100 0101 1010 0111 1110 0110 0110 0011 1100 Task G Tap into your Potential Binary code can be represented by coloured squares with white as 0 and black as 1. 1) What is the binary code that makes up the picture below? Enter the binary code in the answer box below.
Activity 4.2 Number Crunching (convert denary numbers to binary) Denary is the decimal system that humans use this system is called base 10 because there are 10 numbers and it uses the power of 10. The denary system uses 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Task A Become a Convert Denary numbers, such as 0123, need to be converted to binary numbers so that a computer can understand and process them. 1) Convert the denary numbers below to binary. 120... 45... 80... 2) Convert your age to binary. 3) Convert the age of one of your friends into binary code. Task B Picture This In this task you will convert denary numbers to binary and represent the binary numbers as colours. 1) What picture do you get when you convert the following denary numbers to binary and then colours? (Black on and white off) 0 255 153 153 231 231
Task C Alien Race Blurb has devised a race for his friends. They must run a specified distance. Can you work out the distance in km using the binary number 0001 0100 (converting binary to denary)? FINISH 0001 0100 Task D Beat the Clock Bod s internal chronometer runs faster than human time and he's bored as his class appears to be going very slowly. Bod has another 30 minutes to go. 1) Bod uses binary to store data. Help Bod work out how much time is remaining by converting the denary number 30 into binary.
Activity 4.3 Adding Binary To add two denary numbers together we add a number to an existing number. So 1 + 1 2. The binary number for 2 is a 1 and a 0 (10). The binary number for 3 is 11. Task A Sum it Up In the following task you will add binary numbers together. 1) Add the following binary numbers: 00011000 00001111 Task B How to Get Ahead in Robotics There are two parts to this task: first convert measurements to binary and then add two binary numbers together. Scenario: The Automatron needs to repair Bod after his disastrous attempt at base jumping. In order to reassemble him, she needs to know the original height of each part. 1) Work out in binary the measurements shown on the ruler below to help find the measurement of Bod's head including antennae. 9 8 7 6 5 4 3 2 1 0 08 04 02 01
2) Now work out in binary the measurements shown on the ruler below to help find the measurement of Bod's torso and legs. 9 8 7 6 5 4 3 2 1 0 08 04 02 01 3) Now add the two binary measurements shown to find Bod's total height. Task C Eye Robot Scenario: Orb is a school class monitor. He's got his eye on Bod. Orb also has an eye in the back of his head. 1) How many eyes does Orb have? Convert this number to binary. 08 04 02 01 The school has employed another class monitor. This monitor has one eye. In binary that's 0001. 2) Add this binary number to the previous number to work out how many eyes will be following Bod's progress. + 0001 0010
Task D Beat the Clock 2 Add together the binary numbers representing the time remaining and the minutes already spent in class to find the duration of the class (your answer must be in binary format). 30 minutes 00011110 60 minutes + 00111100 Task E Go with the Overflow In the following task you will work with overflow errors. 1) Add the two binary numbers below do you get an overflow error? + 1110011 1010100 Yes No 2) Overflow errors can occur when adding binary numbers. Tick the box below which correctly explains why overflow errors happen. a b c d Overflow errors occur when the result contains fewer digits than the numbers being added together Overflow errors occur when denary numbers are added together Overflow errors occur when the result contains more digits than the numbers being added together Overflow errors only occur when eight binary digits are added together 3) Tick the statement that best describes what can happen when an overflow error occurs. a b c d The computer will work normally with no incorrect answers The computer may crash but answers will always be correct The overflow error may result in an incorrect answer and the computer may crash Overflow errors can cause viruses to enter a computer system
ASCII Character Set Common Printable Characters BINARY DECIMAL CHARACTER 0011 0000 0 0011 0001 1 0011 0010 2 0011 0011 3 0011 0100 4 0011 0101 5 0011 0110 6 0011 1001 7 0011 1000 8 0011 1001 9 0010 0000 32 Space 0010 0001 33! 0010 0010 34 " 0010 0011 35 # 0010 0100 36 $ 0010 0101 37 % 0010 0110 38 & 0010 0111 39 ' 0010 1000 40 ( 0010 1001 41 ) 0010 1010 42 * 0010 1011 43 + 0010 1100 44, 0010 1101 45-0010 1110 46. 0010 1111 47 / 0011 0000 48 0 0011 0001 49 1 0011 0010 50 2 0011 0011 51 3 0011 0100 52 4 0011 0101 53 5 0011 0110 54 6 0011 0111 55 7 0011 1000 56 8 0011 1001 57 9 0011 1010 58 : 0011 1011 59 ;
Common Printable Characters BINARY DECIMAL CHARACTER 0011 1100 60 < 0011 1101 61 0011 1110 62 > 0011 1111 63? 0100 0000 64 @ 0100 0001 65 A 0100 0010 66 B 0100 0011 67 C 0100 0100 68 D 0100 0101 69 E 0100 0110 70 F 0100 0111 71 G 0100 1000 72 H 0100 1001 73 I 0100 1010 74 J 0100 1011 75 K 0100 1100 76 L 0100 1101 77 M 0100 1110 78 N 0100 1111 79 O 0101 0000 80 P 0101 0001 81 Q 0101 0010 82 R 0101 0011 83 S 0101 0100 84 T 0101 0101 85 U 0101 0110 86 V 0101 0111 87 W 0101 1000 88 X 0101 1001 89 Y 0101 1010 90 Z 0101 1011 91 [ 0101 1100 92 \ 0101 1101 93 ] 0101 1110 94 ^ 0101 1111 95 _ 0110 0000 96 ' 0110 0001 97 a 0110 0010 98 b 0110 0011 99 c
Common Printable Characters BINARY DECIMAL CHARACTER 0110 0100 100 d 0110 0101 101 e 0110 0110 102 f 0110 0111 103 g 0110 1000 104 h 0110 1001 105 i 0110 1010 106 j 0110 1011 107 k 0110 1100 108 l 0110 1101 109 m 0110 1110 110 n 0110 1111 111 o 0111 0000 112 p 0111 0001 113 q 0111 0010 114 r 0111 0011 115 s 0111 0100 116 t 0111 0101 117 u 0111 0110 118 v 0111 0111 119 w 0111 1000 120 x 0111 1001 121 y 0111 1010 122 z 0111 1011 123 { 0111 1100 124 0111 1101 125 } 0111 1110 126 ~ 0110 0000 127 DEL
Blank Grids