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 five binary place values, reading from the right?
2. In binary, how is each place value related to the place on its right?
3. What is the place value that comes right after 8 in a binary place value grid?
4. Which place in a binary number is worth the least?
5. In the decimal number 345, the 3 is worth 300. What is the matching idea in binary?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 116 8 4 2 1 | AThe values go up by 1 each time. They should double: 1, 2, 4, 8, 16. | |
| 21, 2, 4, 8, 16 | BThe doubling pattern of binary place values, starting at the right | |
| 3The place value to the left of the 8 column in binary is double 8 | C8 x 2 = 16 | |
| 4Decimal place values grow by 10 times each step, but binary place values double | DDecimal: 1, 10, 100 / Binary: 1, 2, 4 | |
| 5Binary place values: 1, 2, 3, 4, 5 | EAfter 4 the pattern adds 2 instead of doubling. Double 4 is 8, then double 8 is 16. | |
| 6Binary place values: 1, 2, 4, 6, 8 | FThe place values of a 5-bit binary number, written from left to right |
C
Definitions
1, 2, 4, 8, 16
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
Place values: 16, 8, 4, 2, _
2.
Binary places: 1, 2, 4, _, 16
3.
Each place is worth ______
the place to its right
4.
Decimal places: 1, 10, ___, 1000
5.
The place after 16 is 16 x 2 = __
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
# Binary place values
B
values = [1, 2, 3, 4, 5]
C
print(values[0])
Question 2
A
place = 1
B
for i in range(4):
C
place = place + 2
D
print(place) # 16
Question 3
A
bits = [1, 0, 1]
B
places = [4, 2, 1]
C
total = 4 + 2 + 1
D
print(total) # 5
Question 4
A
# Place values for 4 bits
B
p1 = 1
C
p2 = p1 * 2
D
p3 = p2 * 3
E
p4 = p3 * 2
Question 5
A
right_place = 0
B
next_place = right_place * 2
C
print(next_place)
Answer Key
Binary place values
Section A: Quick Questions
Q1
A — 1, 2, 4, 8, 16
Q2
A — It is worth double
Q3
A — 16
Q4
B — The place on the far right, worth 1
Q5
B — Each place has its own value, like 1, 2, 4, 8 or 16
Section B: Match the Pairs
Q1
16 8 4 2 1 → The place values of a 5-bit binary number, written from left to right
Q2
1, 2, 4, 8, 16 → The doubling pattern of binary place values, starting at the right
Q3
The place value to the left of the 8 column in binary is double 8 → 8 x 2 = 16
Q4
Decimal place values grow by 10 times each step, but binary place values double → Decimal: 1, 10, 100 / Binary: 1, 2, 4
Q5
Binary place values: 1, 2, 3, 4, 5 → The values go up by 1 each time. They should double: 1, 2, 4, 8, 16.
Q6
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.
Section C: Definitions
Q1
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.Section D: Fill in the Blanks
Q1
Place values: 16, 8, 4, 2, 1Q2
Binary places: 1, 2, 4, 8, 16Q3
Each place is worth double
the place to its rightQ4
Decimal places: 1, 10, 100, 1000Q5
The place after 16 is 16 x 2 = 32Section E: Spot the Error
Q1
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].
Q2
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.
Q3
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.
Q4
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).
Q5
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.