# How are printed circuit boards designed with letters

## Letter coding using binary representation

### Key questions

• How many different characters can you type on a computer? (Suggestions include the 26 letters of the standard English alphabet, and then moving on to the other characters on the keyboard, including capital letters, numbers, and punctuation. Some students may be aware that other languages ​​can have thousands of characters, and each other with new emoticons, the range of available characters has also increased!)

### Lesson entry

Think about how you would tell another person a letter of the alphabet if the message had to be limited to a number between 0 and 26. (Students mostly suggest using the code 1 for a, 2 for b, etc.)

Use 5 bits to work out and write down the binary numbers for 0 to 26 on the binary to alphabet resource and then add the letters of the alphabet.

### Lesson activities

Using the table the students created earlier, give the students a message to decipher, such as your name or the name of a writer (e.g. 00001 00010 00010 11001 for ABBY).

Then have the students write down and communicate their own messages. Remind them that they can write zeros and ones using any symbols, such as check marks and crosses.

Also consider unusual representations: For example, the individual bits could be communicated using tones that are either high or low. Or the 5-bit number could be represented by holding up five fingers on one hand, with each finger corresponding to one bit.

Some languages ​​have slightly more or fewer characters, including letters with diacritical marks. If students are considering an alphabet with more than 32 characters, 5 bits will not be enough. Some students may have realized that a code is needed for a space (0 is a good choice), so 5 bits only cover 31 alphabetic characters.

Have students design a system that can accommodate a few extra marks, such as diacritical marks. (This can usually be done by assigning larger numbers such as 27 to 31 to the additional characters.)

A typical English language computer keyboard has about 100 characters (this includes uppercase and lowercase letters, punctuation marks, numbers, and special characters). How many bits are needed to assign a unique number to each character on the keyboard? (Usually 7 bits are sufficient, as this allows 128 different codes.)

Now have the students consider larger alphabets. How many bits are required if we want to represent each of the 50,000 Chinese characters by a number? (16 bits allow up to 65,536 different representations.)

### Lesson review

• What are the reasons why we do not use the binary number system as a means of communication for our written language?
• How would the ancient Egyptians have converted their hieroglyphs into a binary representation?