JSS 3 First Term

Learning Objectives

• Distinguish between a bit, a byte and a word.
• Convert between binary and decimal using place value.
• Explain how text, images and sound are stored in binary.
• Use the units of data such as the kilobyte and the megabyte.

Starter Scenario

A market trader uses a simple tally sheet with only two marks, a plain tick and a crossed tick, to count her sold crates each day. With just these two symbols she can record any total, because the position of each mark gives it a value. Computers do something similar, but with only two digits. Instead of many symbols, a computer uses just two states, which we write as 0 and 1. This two symbol system is called binary, and it is the language of all digital devices.

Bits and Bytes

A bit is the smallest piece of data a computer can handle. The word bit comes from binary digit, and a bit is always either 0 or 1. Because one bit only carries two possibilities, computers group bits together. Eight bits make one byte. A byte is enough to hold one letter of text, and modern files are described in bytes, kilobytes, megabytes and gigabytes. Think of a bit as one light switch that is either off or on. A single switch shows only two states, but many switches together can show an enormous number of combinations.

Our everyday numbers are in the decimal system, which is base 10, because it uses ten digits from 0 to 9. Each position in a decimal number is worth ten times the position to its right, so 10, 100 and 1000 are place values. The binary system is base 2, because it uses only two digits, 0 and 1. Each position is worth two times the position to its right, so the place values are 1, 2, 4, 8, 16 and so on. Computers use binary because their circuits have two clear states, such as on or off, high or low voltage, and magnetised or not magnetised. Using two states is simple and reliable for electronics.

Reading Binary Place Values

To understand a binary number, write its place values above the digits from the right. The rightmost position is worth 1, the next is 2, then 4, then 8. Take the binary number 1011. Above it from the right we place 1, 2, 4 and 8. So 1011 means one eight, zero fours, one two and one one, which is 8 plus 2 plus 1, giving decimal 11. To convert this binary to decimal, only add the place values that sit above a 1, giving 8 plus 2 plus 1, which equals 11.

Converting Between Binary and Decimal

To convert binary to decimal, write the binary digits, then label the place values 1, 2, 4, 8 and 16 from right to left. Add only the labels that sit above a 1, and the total is the decimal number. For example, binary 10101 has place values 16, 8, 4, 2 and 1 from left to right. The 1s sit above 16, 4 and 1, so the value is 16 plus 4 plus 1, which is 21.

To convert decimal to binary, find the largest binary place value that fits inside the decimal number, put a 1 there, then subtract. Repeat with the remainder using the next smaller place value, putting a 0 where a place is not used, until you reach the 1s column. For example, to turn 13 into binary, the largest place that fits is 8, so we put a 1 and subtract to get 5. The next place, 4, fits, so we put a 1 and subtract to get 1. The 2s place does not fit, so we put a 0. The 1s place fits, so we put a 1. Reading across we get 1101.

How Text is Stored

Each letter, digit and symbol on a keyboard is given a code number. One common system is ASCII, in which a capital A is 65, a capital B is 66, and so on, and each number is then written in binary. Because a byte has eight bits, it can hold any code from 0 to 255, which is enough for all letters, digits, punctuation and symbols. When you type a word, the computer stores the code of each character one after another, and each character takes about one byte. For example, the word OK would be stored as the code for O, which is 79, and the code for K, which is 75, each written in eight bits.

How Images are Stored

An image on a screen is made of tiny dots called pixels, arranged in rows and columns. Each pixel records a colour, and each colour is stored as a number in binary. In a simple black and white image, a pixel can be a 0 for black and a 1 for white. In a colour image, each pixel keeps separate numbers for the amount of red, green and blue, and those numbers are also stored in binary. The more pixels an image has, the sharper it looks, but the more 0s and 1s it needs, which is why photo files can be large.

How Sound is Stored

Sound is a moving wave in the air. A computer records sound by measuring the wave many times each second and turning each measurement into a number. These measurements are called samples. Each sample is stored in binary, and by replaying the samples in order the device rebuilds the original sound. Recording more samples per second gives better quality but uses more data. So whether the device works with a typed letter, a colourful photo or a recorded song, the process is the same. Everything is turned into numbers, and those numbers are written in binary.

Reading a Simple Binary Message

Using a small code where A equals 1, B equals 2, and so on, each letter can be written in binary and read back by a decoder. For example, A equals 1 in decimal and 1 in binary. B equals 2 in decimal and 10 in binary. C equals 3 in decimal and 11 in binary. D equals 4 in decimal and 100 in binary. Learners should decode the binary message 100, 1, 11, 4 by converting each binary back to decimal and then to a letter to read the hidden word.

Binary Data Representation

Computers store all information using only two digits, 0 and 1. This is the binary system, and every piece of data a computer handles, whether it is a letter, a photograph or a song, is ultimately represented as a long sequence of these two digits. The reason computers rely on binary is that electronic circuits have two clear states such as on and off, high voltage and low voltage, which map perfectly to 1 and 0.

A bit is the smallest unit of data in a computer. The word bit is short for binary digit, and it can hold only one of two values, either 0 or 1. Because a single bit carries so little information, computers group bits together into larger units. A byte is the most common grouping and it consists of exactly eight bits. Eight bits give 256 possible combinations (from 00000000 to 11111111), which is enough to represent one character of text or a small number.

Beyond the byte, computers use words, which are groups of bits that the processor handles in one operation. On a 32-bit computer, a word is 32 bits (four bytes), and on a 64-bit computer, a word is 64 bits (eight bytes). The size of the word affects how fast the computer can process data because a larger word means more data is handled in a single step.

A bit holds a single 0 or 1 and is the fundamental building block of all digital data.

A byte contains eight bits and is the standard unit for measuring data size.

A word is the number of bits a CPU processes in one cycle, commonly 32 or 64 bits on modern computers.

All data inside a computer, including text, images, sound and programmes, is stored as sequences of 0s and 1s.

Storage Metrics and Simple Conversions

Data in a computer is measured using a standard set of units that grow from the very smallest to very large. A bit is the smallest unit, representing a single 0 or 1. Two bits together can represent four different values (00, 01, 10, 11), and four bits form a nibble, which can represent sixteen different values. A nibble is half a byte and is sometimes used when working with hexadecimal numbers.

A byte, made up of eight bits, is the most commonly used unit. One byte can represent 256 different values, which is enough for a single character in many encoding systems. When we need to describe larger amounts of data, we use multiples of bytes. A kilobyte (KB) is 1,024 bytes, a megabyte (MB) is 1,024 kilobytes, a gigabyte (GB) is 1,024 megabytes, and a terabyte (TB) is 1,024 gigabytes. The number 1,024 is used because computers work in binary and 1,024 is 2 to the power of 10.

Understanding these units helps when choosing storage or comparing devices. A typical school essay might be 50 KB, a photograph around 3 MB, a short video clip about 100 MB, and a full-length movie around 4 GB. Internet speeds are often measured in megabits per second (Mbps), while file sizes are usually shown in megabytes (MB). There are eight bits in a byte, so a speed of 8 Mbps can transfer roughly 1 MB of data each second.

1 bit = a single 0 or 1.

4 bits = 1 nibble = 16 possible values.

8 bits = 1 byte = 256 possible values.

1 KB = 1,024 bytes. 1 MB = 1,024 KB. 1 GB = 1,024 MB. 1 TB = 1,024 GB.

Character Encoding, ASCII and Unicode

For a computer to store and display text, every character must first be converted into a number, and that number is then stored in binary. Character encoding is the system that assigns a unique number to each letter, digit, punctuation mark and special symbol. One of the earliest and most well-known encoding systems is ASCII, which stands for American Standard Code for Information Interchange.

The original ASCII system uses seven bits to represent each character, giving 128 possible codes (from 0 to 127). This is enough for all uppercase and lowercase English letters, the digits 0 to 9, common punctuation marks and control characters such as space and line break. For example, the letter A is assigned the code 65, the letter a is 97, and the digit 0 is 48. An extended version of ASCII uses eight bits (one byte), which doubles the available codes to 256, allowing room for additional symbols used in European languages.

As computers spread worldwide, ASCII proved limited because it could not represent characters from languages such as Arabic, Chinese, Hindi or Yoruba. Unicode was created to solve this problem. Unicode assigns a unique code to every character in every writing system, including emojis and mathematical symbols. The most common form of Unicode is UTF-8, which uses one to four bytes per character. UTF-8 is backward compatible with ASCII, meaning that the code for A is still 65, but Unicode can also represent characters far beyond the original 128.

ASCII assigns a 7-bit code (0 to 127) to English letters, digits and common symbols.

Extended ASCII uses 8 bits and supports 256 characters, useful for European languages.

Unicode supports characters from all the world writing systems and uses 1 to 4 bytes per character.

UTF-8 is the most widely used encoding on the internet because it handles both ASCII and non-ASCII characters efficiently.

Character encoding matters because without a shared standard, different computers would interpret the same binary numbers as different characters, leading to garbled text.

Practical Work

1. Convert the binary number 10101 to decimal.
2. Write the codes 65 and 66 in binary to represent A and B.
3. Estimate the size of a photograph in megabytes from its pixels.
4. Decode the binary message 100, 1, 11, 4 using A equals 1.

Scenario-Based Questions

1. A pupil says one byte is the same as one bit. Correct this by explaining the difference between a bit and a byte and giving one example of how many of each is needed to store the letter A.
2. A school asks how much memory is needed to store 200 characters if each character uses 8 bits. Show your working.
3. A market trader uses a tally where a tick means 1 and a crossed tick means 0, just like binary. If the trader writes tick, crossed tick, tick, tick, what decimal number does this represent?
4. A phone camera takes a photo that is 1920 pixels wide and 1080 pixels high. If each pixel uses 3 bytes for colour, estimate the total size of the photo in megabytes.
5. Using ASCII where A equals 65, write the letter A in binary and explain how a computer stores the word CAT.
6. A song is recorded for 60 seconds at a sampling rate of 44,100 samples per second, with each sample using 16 bits. Estimate the size of the recording in megabytes.
7. A school lab has computers that store text in ASCII. A pupil types the word NAIJA. How many bytes are needed to store this word, and how would the computer store the letter N in binary?

LEARNING OBJECTIVES: BY THE END OF THE LESSON PUPILS SHOULD BE ABLE TO:

Rationale: A bit is the smallest piece of data a computer can handle. Understanding starter Scenario, bits and Bytes, reading Binary Place Values, converting Between Binary and Decimal helps learners use digital technology confidently, safely and responsibly.

Pre-requisite Knowledge: In Week 5, learners studied Number Systems, including what is a Number System, the Binary System, converting Decimal to Binary. The knowledge from that week is used again in this lesson.

Learning Material/Teaching Aid: Whiteboard, markers, computer or laptop where available, printed notes and charts on Binary Numbers and Data Representation, practical task sheets, learners' notebooks and pens.

Reference Materials: Digital Technology for Junior Secondary Schools (JSS 3); NERDC Digital Technology Curriculum; Digital Technology JSS 3 First Term Notes (Week 6); First Term examination and Continuous Assessment question papers.

LESSON DEVELOPMENT

Assignment: i. A pupil says one byte is the same as one bit. Correct this by explaining the difference between a bit and a byte and giving one example of how many of each is needed to store the letter A. ii. A school asks how much memory is needed to store 200 characters if each character uses 8 bits. Show your working.