Lesson 2 of 5
Read and write numbers with place values
One idea at a time. Try the example, then keep going.
Big ideas · 1 of 11
Big ideas
Do this: Read each idea. Then say the 4-bit place values out loud: 8, 4, 2, 1.
Decimal uses ten digits, 0 to 9, with place values of 1, 10, 100 and 1000. In 345, the 3 is worth 300 because of where it sits.
Each binary Place valueWhat a digit is worth because of WHERE it sits.Exactly: In binary, the columns from right to left are worth 1, 2, 4, 8, 16, 32, 64 and 128. Each column is worth double the one to its right.Mix-up alert: A 1 in the 8s place is worth 8. A 1 in the 1s place is worth only 1.See this in Key words doubles to the left: 1, 2, 4, 8, 16, 32, 64, 128. In a 4-bit number the places are 8, 4, 2, 1.
To read binary, write the place values above the bits, then add the place values that have a 1. For example, 1010 is 8 + 0 + 2 + 0 = 10.
Go through every place from biggest to smallest: write 1 and subtract when it fits; otherwise write 0. This is how to ConvertChange how a number is WRITTEN without changing how much it is.Exactly: Binary to decimal: add the place values that have a 1. Decimal to binary: take the biggest place value that fits, write 1, subtract, and keep going.Mix-up alert: Converting changes the writing, not the amount. 1011 in binary and 11 in decimal are the same amount.See this in Key words a decimal number to binary. Every place gets a digit, so 6 in 4 bits is 0110, not 011.
4 bits make 16 patterns, for the numbers 0 to 15. We always write the full width, so 6 in 4 bits is 0110.
8 bits make one ByteA group of 8 bits.Exactly: Eight bits handled together. One byte has 256 different patterns, enough for the numbers 0 to 255.Mix-up alert: A byte is 8 bits, not the other way round. A bit is the smaller one.See this in Key words: 256 patterns, for the numbers 0 to 255. A zero in front keeps the full width without adding value.
Step-through
Do this: Step through the picture. Before each step, say what you think comes next.
Here is how to read any binary number. We will read 1011.
Whole picture, 4 steps
4 steps. Tap a number or Show me how it works.
Try it
Do this: Before you flip anything, predict the number. Say it out loud. Then show the total.
The switches show the pattern 1010. What number is it? Predict first, then press Show the total. After that, flip any switch and watch the total change.
Remember: Add the place values that have a 1. That is the number.
Try it
Do this: Flip cards face up to show dots. Try to show exactly 13 dots.
These cards have 16, 8, 4, 2 and 1 dots. A card face up is a 1. A card face down is a 0. Count the dots that are showing.
Remember: Each card has double the dots of the card on its right, just like binary place values.
Do this: Follow each step. Then read 1101 again without looking.
Read 1101.
So 1101 in binary is 13.
Do this: Follow each step. Then check the answer by adding the places.
Write 11 in 4 bits: places 8, 4, 2, 1.
Answer: 1011, since 8 + 2 + 1 = 11.
Do this: Say the eight place values, then follow the steps.
Read 01000001.
So 01000001 is 65. You will meet this byte again in the next topic.
Do this: Before each step, say whether the place value fits in what is left.
Write 75 in 8-bit binary. The places are 128, 64, 32, 16, 8, 4, 2, 1.
The answer is 01001011 (64 + 8 + 2 + 1 = 75).
Do this: Read 1010 the binary way and say the number.
1010 in binary is not one thousand ten. Binary places are worth 8, 4, 2 and 1, not 1000, 100, 10 and 1, so 1010 is 8 + 0 + 2 + 0 = 10. Tip: say binary digit by digit, one zero one zero.
Do this: Say why 0110 and 110 have the same value.
0110 is not a bigger number than 110: both are 4 + 2 = 6. A zero in front adds nothing, but we still write it, so every number has the full width: 4 bits or 8 bits.
From other sites
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Watch from 2:05 to 3:03
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Watch from 1:43 to 3:33
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Try it
Do this: Build each number with the switches, then read each pattern. Check after each one.
First, build each number by flipping switches. Then read the patterns and type their numbers.
Remember: Biggest place first when you build. Add the 1s when you read.
Try it
Do this: Use all eight places. Start with the biggest place that fits.
Now the switches are a whole byte: 128, 64, 32, 16, 8, 4, 2, 1. Build each number, then read each pattern.
Remember: One byte can show any whole number from 0 to 255.
Try it
Do this: Show exactly the number of dots asked for, then check.
Flip the 16, 8, 4, 2 and 1 cards to show each number of dots.
Remember: The cards face up and face down are the number in binary.
Try it
Do this: Answer, check, then keep going.
Turn binary into decimal and back. Show the working if you get stuck.
Streak: 0 correct in a row. This session only.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| Blank | Blank | Blank | Blank | Blank | Blank | Blank | Blank |
Work it out on paper if it helps.
Write it
Do this: Write two or three sentences. Show your working, then compare.
Start here if it helps: In binary, the places are worth...
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Flashcards
Do this: Work out each answer before you flip. Mark the ones you still need to learn.
Card 1 of 16
0 Know it0 Still learning
Start at 1 on the right and double.
On the card: Enter or Space flips. Left and Right move. After revealing, 1 marks Still learning and 2 marks Know it. Tab reaches every control.
What are the place values in a 4-bit number?
8, 4, 2, 1 from left to right. Start at 1 on the right and double each time you move left.
What are the place values in an 8-bit number?
128, 64, 32, 16, 8, 4, 2, 1. Start at 1 on the right and keep doubling as you move left.
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| 0 | 1 | 1 | 1 |
What is 0111 in decimal?
7, because 0 + 4 + 2 + 1 = 7.
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| 1 | 0 | 0 | 1 |
What is 1001 in decimal?
9, because 8 + 0 + 0 + 1 = 9.
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| Blank | Blank | Blank | Blank |
Work it out on paper if it helps.
Write 6 in 4-bit binary.
0110, because 4 + 2 = 6.
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| Blank | Blank | Blank | Blank |
Work it out on paper if it helps.
Write 9 in 4-bit binary.
1001, because 8 + 1 = 9.
What is the biggest number 4 bits can show?
15, written 1111: 8 + 4 + 2 + 1.
What is the biggest number 8 bits can show?
255, written 11111111. Every place has a 1: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.
How many patterns can 8 bits make?
256, for the numbers 0 to 255. Each extra bit doubles the count: 2, 4, 8, 16, 32, 64, 128, 256.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
What is 00001010 in decimal?
10. The zeros in front add nothing: 8 + 2 = 10.
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
What is 1111 in decimal?
15, because 8 + 4 + 2 + 1 = 15.
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| Blank | Blank | Blank | Blank |
Work it out on paper if it helps.
Write 13 in 4-bit binary.
1101, because 8 + 4 + 1 = 13.
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| Blank | Blank | Blank | Blank |
Work it out on paper if it helps.
Write 2 in 4-bit binary.
Only the 2s place is needed. Under 8, 4, 2, 1 write 0, 0, 1, 0: 0 + 0 + 2 + 0 = 2. So the pattern is 0010.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
What is 00100000 in decimal?
The only 1 is in the 32s place, so the total is 32.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
What is 11001000 in decimal?
200, because 128 + 64 + 8 = 200.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| Blank | Blank | Blank | Blank | Blank | Blank | Blank | Blank |
Work it out on paper if it helps.
Write 50 in 8-bit binary.
00110010, because 32 + 16 + 2 = 50.
True or false
Do this: Choose True or False. Work it out before you choose.
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| 1 | 0 | 1 | 0 |
Self-test
Do this: Answer every question. Use the place-value table above the bits.
8 questions. One at a time.
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Match
Do this: Choose a word, then choose its meaning.
Connect the ideas
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Classwork
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