# Binary code numbers and letters

There is also an online interactive version of the binary cards herefrom the Computer Science Field Guidebut it is preferable to work with physical cards. Discuss how you would communicate a letter of the alphabet to someone if all you could do is say a number between 0 and Students will usually suggest using a code of 1 or a, 2 for b, and so on.

Work out and write down the binary numbers using 5 bits from 0 to 26 on the Binary to Alphabet resource, then add the letters of the alphabet. Using the table that students have created above, give them a message to decode, such as your name or the name of a book author e. Now get students to write and communicate their own messages. Remind them that they can write the zeroes and ones using any symbols, such as ticks and crosses.

Consider unusual representations; for example, each bit could be communicated with a sound that is either high pitched or low pitched. Or the 5-bit number could be represented by holding up the five fingers on one hand, one finger corresponding to each bit. Some languages have slightly more or fewer characters, which might include those with diacritic marks.

If students consider an alphabet with more than 32 characters, then 5 bits won't be sufficient. Also, students may have realised that a code is needed for a space 0 is a good choice for thatso 5 bits only covers 31 alphabet characters.

Have the students design a system that can handle a few extra characters such as diacritics. This can usually be done by allocating larger numbers, such as 27 to 31, to the other characters.

A typical English language computer keyboard has about characters which includes capital and lowercase letters, punctuation, digits, and special symbols. How many bits are needed to give a unique number to every character on the keyboard?

Typically 7 bits will been enough since it provides different codes. Now have students consider larger alphabets. How many bits are needed if you want a number for each of 50, Chinese characters? It may be a surprise that only 16 bits is needed for tens of thousands of characters.

This is because each bit doubles the range, so you don't need to add many bits to cover a large alphabet. This is an important property of binary representation that students should become familiar with. The rapid increase in the number of different values that can be represented as bits are added is exponential growth i. After doubling 16 times we can represent 65, different values, and 20 bits can represent over a million different values.

Exponential growth is sometimes illustrated with folding paper in half, and half again. After these two folds, it is 4 sheets thick, and one more fold is 8 sheets thick.

In fact, around 6 or 7 folds is already impossibly thick, even with a large sheet of paper. Using a 5-bit code for an alphabet goes back to at least the "Baudot" code ; many different number to letter correspondences have been used over the years to represent alphabets, but one that was common for some time is "ASCII", which used 7 bits and therefore could represent over different characters.

These days "Unicode" is common, which can represent overdifferent characters. Nevertheless, each of these codes, including Unicode, still contain elements of the simple code used in this lesson A is 1, B is Throughout the lessons there are links to computational thinking. Below we've noted some general links that apply to this content. Teaching computational thinking through CSUnplugged activities supports students to learn how to describe a problem, identify what are the important details they need to solve this problem, and break it down into small, logical steps so that they can then create a process which solves the problem, and then evaluate this process.

These skills are transferable to any other curriculum area, but are particularly relevant to developing digital systems and solving problems using the capabilities of computers. For more background information on what our definition of Computational Thinking see our notes about computational thinking. We used two algorithms in this lesson: These are algorithms because they are a step-by-step process that will always give the right solution for any input you give it as long as the process is followed exactly.

Choose a letter to convert into a decimal number. A more efficient algorithm would have a table to look up, like the one created at the start of the activity, and most programming languages can convert directly from characters to numbers, with the notable exception of Scratch, which needs to use the above algorithm.

The next algorithm is the same algorithm we used in lesson 1, which we use to convert a decimal number to a binary number:. Have students create instructions for, or demonstrate, converting a letter into a decimal number with or without the tableand then convert a decimal number into binary; are they able to show a systematic solution? Can they explain what they are doing at each step and why? This activity is particularly relevant to abstraction, since we are representing written text with a simple number, and the number can be represented using binary digits, which, as we know from lesson 1, are an abstraction of the physical electronics and circuits inside a computer.

We could also expand our abstraction because we could use any two symbols other than 0s and 1s to represent our message although while students are first learning this we recommend sticking with 1s and 0s.

For example, you could represent your message by flashing a torch on and off this gives an idea of how information might be sent over a fibre-optic cable! Binary number representation is an abstraction that hides the complexity of the electronics and hardware inside a computer that stores data.

When you use a different representation for binary, such as turning the torch on and off, who are the students who quickly see that this is equivalent to when they previously used 0s and 1s? They will probably feel comfortable working with this new representation quickly, and other students may be very confused by this change. Look for students who then decide to create their own representations of binary numbers.

The core example of decomposition in this activity is understanding that in computing we have to break down all information into tiny chunks so that computers can store and send this data as bits and bytes. Everything we store inside a computer and see appear on the screen has to have been, in some way, broken down into binary digits.

In this lesson students have performed several steps of decomposition as they have taken the task of encoding a message and broken it down into simple steps. To write a message in binary we have to first look at the message one letter at a time and convert each of these, one-by-one, into decimal numbers, and then convert each of these numbers, one-by-one, into binary numbers.

Students perform these same steps in reverse to convert the message back to text. Can students explain why it is important that we can use binary to represent letters?

Ask them why it is useful each separate letter into binary, rather than choosing a decimal and binary number for each different word. Recognising patterns in the way the binary number system works helps give us a deeper understanding of the concepts involved, and assists us in generalising these concepts and patterns so that we can apply them to other problems.

Have students decode a binary message from another student, by converting the binary numbers into decimal numbers, and then to text to view the message. Ask them what they would do if they wanted to include other characters in their message: What if we want to use exclamation and question marks? Observe which students see that we can simply generalise the method they are already using and can match other characters to bigger decimal numbers, e.

If we can represent 32 different characters in binary when we use 5 bits for each character, then how many would we need for 64? Which students can see the pattern of binary and doubling in this situation, and see that we simply need to use 1 more bit to do this?

Logical thinking involves making decisions based on knowledge you have, and these decisions should be sensible and well thought out. If you memorise that the letter H is represented as binary it's not as useful as learning how to represent any character using the process described in this activity.

If you can understand the logical steps we take as we convert a letter into a binary number, and how we can convert it back, then you will be able to represent any character as binary, and more importantly, you understand the process, since you're more likely to get a computer to do it for you rather than always do it manually.

This is especially relevant if we want to represent a large number of characters. What if we wanted to represent every Chinese character? There are over 50, of them so trying to memorise them all would take a long time! Observe the systems students have created to translate their letters into binary and vice versa. What logic has been applied to these? Are they efficient systems? Can they explain what they are doing at each step?

Ask students why we are using the numbers 1 to 26 to represent our letters, or if they think there could be a better choice. Ask them how they would choose numbers for other characters, such as choosing a number to represent a space. Which ones give logical answers and can explain why their solution is a good choice? An example of evaluation is working out how many different characters can be represented by a given number of bits e.

When thinking about how many bits to use to represent something Computer Scientists also have to think about are how much space this is going to take up on a computer bit characters take up twice the space of 8-bit charactersand if we should have some extra bits in case we want to add more characters in the future.

Evaluating the benefits and costs of using a certain number of bits is also an idea students can explore.

Can a student work out how many bits are needed to represent the characters in a language with characters? Home Topics Binary numbers Binary numbers Codes for letters using binary representation Codes for letters using binary representation Duration: Printables Binary Cards One set for class demonstration. Binary Cards Small One set of cards per student. Binary to Alphabet Blank sheets for students, plus teacher answer sheet. Table of contents Codes for letters using binary representation Key questions Lesson starter Lesson activities Adding more characters Lesson reflection Computational Thinking.

Learning outcomes Students will be able to: Create your own message by converting alphabet characters to decimal numbers then to binary. Decomposition Discuss why it's important to be able to store more than the standard English alphabet. Language Learning Explain how codes for larger alphabets could be created that also include capital letters, punctuation, symbols and diacritics e.

Generalising and Patterns Interpret a message using binary. Generalising and Patterns Recognise how computers represent alphabet characters as bits using a simplified method. Check their binary code for three is as students commonly write as they anticipate the pattern without necessarily checking it is correct.

Check they are writing the binary code in the correct order with the least significant value on the right - for example some will start with one as instead of Check that all students can describe back to you how to calculate the number they are up to. This will identify those who are guessing the pattern. Note that if your local alphabet is slightly different e.

The next algorithm is the same algorithm we used in lesson 1, which we use to convert a decimal number to a binary number: Find out the number of dots that is to be displayed.

We'll refer to this as the "number of dots remaining", which initially is the total number to be displayed.

Finally, even though we're giving point values to each of those lightbulbs, when we binary code numbers and letters them down we still only write them as ones and zeros. One means On, and Zero means Off. So let's say we had 8 lightbulbs, and they were set up like this: The point values of those eight bulbs are: And that adds up to So we would say the sequence of bulbs is worth But how do we write it? We write it like this: And that's Binary Code.

Go ahead and enter some text into the encoder. The computer will convert those letters into numbers, and then it will convert those numbers into binary! So a word with 5 letters would take 40 lightbulbs! How many binary code numbers and letters do you think it took to make this page?

I bet it was a lot! Enter some text here to be converted to binary. Basic Explanation Did you know that everything a computer does is based on ones and zeroes? It's hard to imagine, because you hear people talking about the absolutely gargantuan huge numbers that computers "crunch".

But all those huge numbers - they're just made up of ones and zeros. It's kind of like the computer is made up of a bunch of lightswitches, and each lightswitch controls just one lightbulb.

What do I mean by sequence? Let's say you had two lightswitches. There are four different ways we could flip those switches: We'll say the first lightbulb is worth two points, and the second one is worth one point. Now take a look at the combinations: As you can see, it's going to take a lot of lightbulbs to make a really big number! Binary code numbers and letters those two numbers are represented by lightbulbs, what is the value assigned to a bulb that is not turned on?

What would be another way to write this: On Off On On Off? If you convert your name to binary using the encoder, what is the result? If you convert a 5-letter word to binary, how many digits does the result have? Assign this reference page. Match color, font, and letter in this strategy game. Reviews and book lists - books we love!

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A binary code represents textcomputer processor instructionsor any other data using a two-symbol system. The two-symbol system used is often the binary number system 's 0 and 1.

The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary string of eight bits can represent any of possible binary code numbers and letters and can therefore represent a wide variety of different items. In computing and telecommunications, binary codes are used for various methods of encoding data, such as character stringsinto bit strings.

Those methods may use fixed-width or variable-width strings. In a fixed-width binary code, each letter, digit, or other character is represented by a bit string of the same length; that bit string, interpreted as a binary numberis usually displayed in code tables in octaldecimal or hexadecimal notation.

There are many character sets and many character encodings for them. A bit string, interpreted as a binary number, can be translated into a decimal number. For example, the lower case aif represented by the bit string as it is in the standard ASCII codecan also be represented as the decimal number The full title is translated into English as the "Explanation of the binary arithmetic", which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi.

Leibniz's system uses 0 and 1, like the modern binary numeral system. Leibniz encountered the I Ching through French Jesuit Joachim Bouvet binary code numbers and letters noted with fascination how its hexagrams correspond to the binary numbers from 0 toand concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired.

Binary numerals were central to Leibniz's theology. He believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. The book had confirmed his theory that life could be simplified or reduced binary code numbers and letters to a series of straightforward propositions. He created a system consisting of rows of zeros and ones.

During this time period, Leibniz had not yet found a use for this system. Binary systems predating Leibniz also existed in the ancient world. The residents of the island of Mangareva in French Polynesia were using a hybrid binary- decimal binary code numbers and letters before The ordering is also the lexicographical order on sextuples of elements chosen from a binary code numbers and letters set. In Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text.

Another mathematician and philosopher by the name of George Boole published a paper in called 'The Mathematical Analysis of Logic' that describes an algebraic system of logic, now known as Boolean algebra.

Shannon wrote his thesis inwhich implemented his findings. Shannon's thesis became a starting point for the use of the binary code in practical applications such as computers, electric circuits, and more. The bit string is not the only binary code numbers and letters of binary code. A binary system in general is any system that allows only two choices such binary code numbers and letters a switch in an electronic system or a simple true or false test.

Braille is a type of binary code that is widely used by blind people to read and write by touch, named for its creator, Louis Braille. This system consists of grids of six dots each, three per column, in which each dot has two states: The different combinations of raised and flattened dots are capable of representing all letters, numbers, and punctuation signs. The binary code numbers and letters are diagrams used in feng shuiTaoist cosmology and I Ching studies.

The relationships between the trigrams are represented in two arrangements, the primordial, "Earlier Heaven" or "Fuxi" baguaand the manifested, "Later Binary code numbers and letters "King Wen" bagua.

In Yoruba religionthe rite provides a means of communication with spiritual divinity. In wood powder, these are recorded as single and double lines. The American Standard Code for Information Interchange ASCIIuses a 7-bit binary code to represent text and other characters within computers, communications equipment, and other devices. Each letter or symbol is assigned a number from 0 to **binary code numbers and letters** For example, lowercase "a" is represented by as a bit string which is 97 in decimal.

Binary-coded decimalor BCD, is a binary encoded representation of integer values that uses a 4-bit nibble to encode decimal digits. Four binary bits can encode up to 16 distinct values; binary code numbers and letters, in BCD-encoded numbers, only the first ten values in each nibble are legal, and encode the decimal digits zero, through nine. The remaining six values are illegal, and may cause either a machine exception or unspecified behavior, depending on the computer implementation of BCD arithmetic.

BCD arithmetic is sometimes preferred to floating-point numeric formats in commercial and financial applications where the complex rounding behaviors of floating-point numbers is inappropriate. Most modern computers use binary encoding for instructions and data. Telephone calls are carried digitally on long-distance and mobile phone networks using pulse-code modulationand on voice over IP networks. The weight of a binary code, as defined in the table of constant-weight codes[18] is the Hamming weight of the binary words coding for the represented words or sequences.

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Leibniz, Mysticism and Religion. Proceedings of the National Academy of Sciences. Philosophy East and West. University of Hawaii Press. The I Ching or Book of Changes.

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