Lesson
Two digits. Countless uses.
TClever TechnologyUnderstand how two digits can represent information.
Digital technology · Explore binary, a system that uses 0 and 1 to represent numbers and information.
Question
How can a computer work with information using only zeros and ones?
How can a computer work with information using only zeros and ones?Answer
Binary is a number system with two digits: 0 and 1. A bit is a binary digit. Combinations of bits can represent numbers and, through agreed-upon codes, text, pictures, and sounds.
Binary is a number system with two digits: 0 and 1. A bit is a binary digit. Combinations of bits can represent numbers and, through agreed-upon codes, text, pictures, and sounds.History
In 1703, Gottfried Wilhelm Leibniz wrote an explanation of binary arithmetic. The mathematics came long before the electronic computers that would put it to widespread use.
In 1703, Gottfried Wilhelm Leibniz wrote an explanation of binary arithmetic. The mathematics came long before the electronic computers that would put it to widespread use.Example
Our familiar place values grow by tens: 1, 10, 100. Binary place values grow by twos: 1, 2, 4, 8. In the binary number 1011, the 1s select 8, 2, and 1. Add them to get eleven.
Our familiar place values grow by tens: 1, 10, 100. Binary place values grow by twos: 1, 2, 4, 8. In the binary number 1011, the 1s select 8, 2, and 1. Add them to get eleven.Insight
A zero still matters. It holds a place and tells us that its value is not included. In 1011, the zero means we do not add the 4.
A zero still matters. It holds a place and tells us that its value is not included. In 1011, the zero means we do not add the 4.Connection
Understanding bits helps us see that digital technology follows rules we can investigate. The tools may be complex, but their foundations can be learned one step at a time.
Understanding bits helps us see that digital technology follows rules we can investigate. The tools may be complex, but their foundations can be learned one step at a time.Challenge
Label four cards 8, 4, 2, and 1 from left to right. Use a 1 for each selected value and a 0 for each unused value. Make eleven, then six and nine. Check after trying: six = 0110; nine = 1001. Explain one zero.
Label four cards 8, 4, 2, and 1 from left to right. Use a 1 for each selected value and a 0 for each unused value. Make eleven, then six and nine. Check after trying: six = 0110; nine = 1001. Explain one zero.
Dive deeper
Context
Binary is a place-value system. Decimal uses ten digits and places worth 1, 10, 100, and so on; binary uses two digits and places worth 1, 2, 4, 8, and so on.
Understand the idea
A 1 includes a place’s value and a 0 leaves it out. Read 1011 using places 8, 4, 2, 1: 8 + 0 + 2 + 1 = 11. Leading zeros do not change that value, so 0011 and 11 both represent three in binary.
Four bits have 16 possible patterns. If those patterns represent unsigned whole numbers, they cover 0 through 15. Bits can also represent letters or pictures, but only when a code tells us how to interpret the pattern.
Try counting past the limit
- Use four cards labeled 8, 4, 2, and 1. Write the binary patterns for 0 through 5.
- Make 15. Explain why every card is selected. Try to make 16 using only those four places.
- Add a new place worth 16 on the left. Show 16 as 10000 and 17 as 10001. Explain why another place was needed.
Discuss together
- Why is the zero in 1011 important?
- Could the same bit pattern stand for a number in one code and a letter in another? What information would you need to know?
Introducing Microlessons
One idea. Seven steps. A practical discovery.
Begin with a question and a clear answer. Explore the history, an example, and a deeper insight. Connect the idea to everyday life, then put it into practice.
Read on your own or talk it through together. Each prepared edition includes a shareable image, concise text, and a one-page PDF.
How the 7 steps work
Each lesson moves from curiosity to understanding to practical action. Here is what each step contributes.
Question
Opens a question worth exploring and gives the lesson a clear purpose.
Answer
Gives a clear starting point that the rest of the lesson helps us understand.
History
Shows how people encountered the idea and how their discoveries shaped what we know.
Example
Makes the idea concrete through a situation, demonstration, or worked example.
Insight
Draws out the deeper principle so we understand why the idea matters.
Connection
Connects the idea to other disciplines, our faith, and everyday life.
Challenge
Turns understanding into action through something to try, practice, or explain.