← Years 5–6 Data & Information

Binary place values

Binary place values. Each position is worth double the one to its right, so reading from the right the values are 1, 2, 4, 8, 16. Decimal doubles into tens instead.

Part of: 5-6 Digital Technologies Vic Curric - Data, Information and Privacy — Module 7, 7-8 Digital Technologies: Representing data with binary — Module 6, IGCSE Computer Science 0478 — 1.1 Number Systems — Module 5, ACARA Digital Technologies Years 7–8 — Representing Text, Images and Sound — Module 8

Understanding Binary place values in Years 5–6 Data & Information

What it does: Each binary position is worth double the position to its right, so the column next to 8 is worth 8 x 2 = 16. 8 doubled is 16, so 16 is the next place. 10 would not follow the doubling pattern. The biggest value is on the left. Reading from the left, the values halve: 8, 4, 2, 1. Each number is double the one before it: 1 doubled is 2, 2 doubled is 4, 4 doubled is 8, and 8 doubled is 16. The pattern starts well with 1, 2, 4 but then stops doubling. The correct values are 1, 2, 4, 8, 16.

Common mistakes: Binary place values double each time: 1, 2, 4, 8, 16. Counting up by 1 (1, 2, 3, 4, 5) is not the doubling pattern. It should be values = [1, 2, 4, 8, 16]. Each binary place is double the one before it, so the loop must multiply by 2. Adding 2 gives 3, 5, 7 and so on. It should be place = place * 2.

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This module's key terms are also in a printable crossword (Modules 1–10) and word search (Modules 1–20).

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Learning
Duo
Which list shows the first five binary place values, reading from the right?
1, 2, 4, 8, 161, 2, 3, 4, 5
Matches
Binary place values: 1, 2, 3, 4, 5
↓
The values go up by 1 each time. They should double: 1, 2, 4, 8, 16.
Applying
Meanings
Term
1, 2, 4, 8, 16
Meaning
Binary place values. Each position is worth double the one to its right, so reading from the right the values are 1, 2, 4, 8, 16. Decimal doubles into tens instead.
Practice
Binary places: 16 8 4 2 1
Testing
Gaps
Place values: 16, 8, 4, 2,
Check Answer
Spots
1# Binary place values
2values = [1, 2, 3, 4, 5]

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Quick Questions

1. Which list shows the first five binary place values, reading from the right?
A. 1, 2, 4, 8, 16 ✓
B. 1, 2, 3, 4, 5
Each place is worth double the one to its right: 1, 2, 4, 8, 16. It does not go up by one each time.
2. In binary, how is each place value related to the place on its right?
A. It is worth double ✓
B. It is worth ten times as much
Binary place values double each time. Ten times as much is how decimal place values work.
3. What is the place value that comes right after 8 in a binary place value grid?
A. 16 ✓
B. 10
8 doubled is 16, so 16 is the next place. 10 would not follow the doubling pattern.
4. Which place in a binary number is worth the least?
A. The place on the far left, worth 1
B. The place on the far right, worth 1 ✓
We start from the right with 1 and double as we move left. The far left place is worth the most.
5. In the decimal number 345, the 3 is worth 300. What is the matching idea in binary?
A. Every place in a binary number is worth the same
B. Each place has its own value, like 1, 2, 4, 8 or 16 ✓
Both decimal and binary use place value. The position of a digit decides how much it is worth.

Match the Pairs

16 8 4 2 1 → The place values of a 5-bit binary number, written from left to right
1, 2, 4, 8, 16 → The doubling pattern of binary place values, starting at the right
The place value to the left of the 8 column in binary is double 8 → 8 x 2 = 16
Decimal place values grow by 10 times each step, but binary place values double → Decimal: 1, 10, 100 / Binary: 1, 2, 4
Binary place values: 1, 2, 3, 4, 5 → The values go up by 1 each time. They should double: 1, 2, 4, 8, 16.
Binary place values: 1, 2, 4, 6, 8 → After 4 the pattern adds 2 instead of doubling. Double 4 is 8, then double 8 is 16.

Key Term

1, 2, 4, 8, 16
Binary place values. Each position is worth double the one to its right, so reading from the right the values are 1, 2, 4, 8, 16. Decimal doubles into tens instead.

Fill in the Blanks

1. Place values: 16, 8, 4, 2, 1
Hint: Type the value of the rightmost place in a binary number
2. Binary places: 1, 2, 4, 8, 16
Hint: Type the missing number, which is double the place before it
3. Each place is worth double the place to its right
Hint: Type the word that describes how each place compares to the one on its right
4. Decimal places: 1, 10, 100, 1000
Hint: Type the missing decimal place value, which is ten times the one before it
5. The place after 16 is 16 x 2 = 32
Hint: Type the result of doubling the biggest place value shown

Spot the Error

Question 1
A # Binary place values
B values = [1, 2, 3, 4, 5]
C print(values[0])
Line B — Binary place values double each time: 1, 2, 4, 8, 16. Counting up by 1 (1, 2, 3, 4, 5) is not the doubling pattern. It should be values = [1, 2, 4, 8, 16].
Question 2
A place = 1
B for i in range(4):
C place = place + 2
D print(place) # 16
Line C — Each binary place is double the one before it, so the loop must multiply by 2. Adding 2 gives 3, 5, 7 and so on. It should be place = place * 2.
Question 3
A bits = [1, 0, 1]
B places = [4, 2, 1]
C total = 4 + 2 + 1
D print(total) # 5
Line C — The middle bit is 0, so the 2 place is not counted. Only the places with a 1 are added: total = 4 + 0 + 1, which gives 5.
Question 4
A # Place values for 4 bits
B p1 = 1
C p2 = p1 * 2
D p3 = p2 * 3
E p4 = p3 * 2
Line D — Each place is worth double the place to its right. p3 should be p2 * 2 (which is 4), not p2 * 3 (which is 6).
Question 5
A right_place = 0
B next_place = right_place * 2
C print(next_place)
Line A — The place on the far right of a binary number is worth 1. If it were 0, doubling would only ever give 0. It should be right_place = 1.

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