Powers of 2 as binary place values
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. Which list shows the first four binary place values, starting from the right?
2. How do you find the next binary place value after 16?
3. What is 2^3 (2 to the power of 3)?
4. What is the value of the place 2^0?
5. Which place value comes between 32 and 128 in the binary table?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 12^3 = 8 | AThe fourth binary place value from the right, found by multiplying 2 by itself three times | |
| 21, 2, 4, 8, 16, 32, 64, 128 | B2^3 was worked out as 2 x 3. It means 2 x 2 x 2, so the answer is 8. | |
| 3To extend the place value table, double the last value | CThe first eight binary place values, each double the one before | |
| 4Binary is called base 2 because every place value is a power of 2 | DThe values go up by 1 each time, but binary place values double each time. It should be 1, 2, 4, 8, 16, 32, 64, 128. | |
| 5Binary place values: 1, 2, 3, 4, 5, 6, 7, 8 | E64 x 2 = 128 | |
| 62^3 = 6 | F2^0, 2^1, 2^2, 2^3 |
C
Definitions
powers of 2
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
2^0 = _
2.
1, 2, 4, 8, __, 32, 64, 128
3.
place ← 1
place ← place _ 2
4.
2^_ = 128
5.
Binary is base _: each place doubles
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
place = 0
B
print(place)
C
place = place * 2
D
print(place)
Question 2
A
place = 1
B
place = place + 2
C
print(place)
Question 3
A
values = [1, 2, 4, 8]
B
last = values[3]
C
next = last * 3
D
print(next)
Question 4
A
places = []
B
p = 1
C
for i in range(8):
D
places.append(i)
E
p = p * 2
Question 5
A
bits = 8
B
biggest = 2 ** bits
C
print(biggest)
Answer Key
Powers of 2 as binary place values
Section A: Quick Questions
Q1
A — 1, 2, 4, 8
Q2
B — Double 16 to get 32
Q3
A — 8
Q4
A — 1
Q5
B — 64
Section B: Match the Pairs
Q1
2^3 = 8 → The fourth binary place value from the right, found by multiplying 2 by itself three times
Q2
1, 2, 4, 8, 16, 32, 64, 128 → The first eight binary place values, each double the one before
Q3
To extend the place value table, double the last value → 64 x 2 = 128
Q4
Binary is called base 2 because every place value is a power of 2 → 2^0, 2^1, 2^2, 2^3
Q5
Binary place values: 1, 2, 3, 4, 5, 6, 7, 8 → The values go up by 1 each time, but binary place values double each time. It should be 1, 2, 4, 8, 16, 32, 64, 128.
Q6
2^3 = 6 → 2^3 was worked out as 2 x 3. It means 2 x 2 x 2, so the answer is 8.
Section C: Definitions
Q1
powers of 2 — Binary place values: 1, 2, 4, 8, 16, 32, 64, 128 and so on. Each place is double the one before it, which is why binary is called base 2.Section D: Fill in the Blanks
Q1
2^0 = 1Q2
1, 2, 4, 8, 16, 32, 64, 128Q3
place ← 1
place ← place * 2Q4
2^7 = 128Q5
Binary is base 2: each place doublesSection E: Spot the Error
Q1
A — The first binary place value is 1, not 0. Doubling 0 would give 0 forever. It should be place = 1.
Q2
B — Each binary place value is double the one before, so we multiply by 2. Adding 2 gives 3, which is not a power of 2. It should be place = place * 2.
Q3
C — To extend the table you double the last value (8 x 2 = 16). Multiplying by 3 gives 24, which is not a binary place value. It should be next = last * 2.
Q4
D — The list should store the place values 1, 2, 4, 8 and so on, held in p. Adding i stores 0, 1, 2, 3 instead. It should be places.append(p).
Q5
B — With 8 bits the places run from 2^0 up to 2^7, so the biggest place value is 2 ** (bits - 1), which is 128. 2 ** bits would give 256.