Counting in binary from 8 to 15 (Representing Text, Images and Sound)
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. What is the number 8 written in 4-bit binary?
2. Which binary number comes right after 1001 (9)?
3. How often does the rightmost column change as you count up?
4. What is 1111 in decimal?
5. Why can't 3 bits show the number 8?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 11000 | AThe number 8: the fourth bit turns on after 0111 (7) and the other three bits reset to 0 | |
| 21111 | B1000 -> 1001 | |
| 3The rightmost column flips between 0 and 1 on every single number, so 9 follows 8 like this | C1010 1011 | |
| 4The second column from the right flips every 2 numbers, so it stays the same for two numbers then changes (10 and 11 both have 1 there) | D1010 is 10. Twelve is 1100, because the 8 and 4 columns are on and the 2 and 1 columns are off. | |
| 58 = 0111 | EThe biggest number four bits can show: 15 | |
| 612 = 1010 | F0111 is 7, not 8. To count 8 you need a fourth bit, so 8 is 1000. |
C
Definitions
0000 to 1111
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
7 = 0111
8 = ____
2.
8 = 1000
9 = ____
3.
12 = 1100
13 = 1101
14 = ____
4.
10 = 1010
11 = 101_
5.
Four bits count from 0000 to ____
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
8 = 1000
B
9 = 1010
C
10 = 1010
Question 2
A
11 = 1011
B
12 = 1100
C
13 = 1110
Question 3
A
Bit 1 flips every number
B
Bit 2 flips every 4 numbers
C
Bit 4 flips every 4 numbers
Question 4
A
Rightmost column, 8 to 11:
B
8 ends in 0, 9 ends in 1
C
10 ends in 0, 11 ends in 0
Question 5
A
Four bits count 0 to 15
B
Smallest: 0001
C
Largest: 1111
Answer Key
Counting in binary from 8 to 15 (Representing Text, Images and Sound)
Section A: Quick Questions
Q1
A — 1000
Q2
A — 1010
Q3
A — Every number (0, 1, 0, 1...)
Q4
B — 15
Q5
B — 3 bits only go up to 111, which is 7
Section B: Match the Pairs
Q1
1000 → The number 8: the fourth bit turns on after 0111 (7) and the other three bits reset to 0
Q2
1111 → The biggest number four bits can show: 15
Q3
The rightmost column flips between 0 and 1 on every single number, so 9 follows 8 like this → 1000 -> 1001
Q4
The second column from the right flips every 2 numbers, so it stays the same for two numbers then changes (10 and 11 both have 1 there) → 1010 1011
Q5
8 = 0111 → 0111 is 7, not 8. To count 8 you need a fourth bit, so 8 is 1000.
Q6
12 = 1010 → 1010 is 10. Twelve is 1100, because the 8 and 4 columns are on and the 2 and 1 columns are off.
Section C: Definitions
Q1
0000 to 1111 — Four bits count from 0 to 15. After 0111 (7) the fourth bit turns on, so 8 is 1000. Each column flips half as often as the column to its right, and the rightmost column flips every number.Section D: Fill in the Blanks
Q1
7 = 0111
8 = 1000Q2
8 = 1000
9 = 1001Q3
12 = 1100
13 = 1101
14 = 1110Q4
10 = 1010
11 = 1011Q5
Four bits count from 0000 to 1111Section E: Spot the Error
Q1
B — 9 is 8 + 1, so it is 1001. The pattern 1010 is the code for 10, not 9.
Q2
C — 13 is 8 + 4 + 1, so it is 1101. The pattern 1110 is 14.
Q3
B — Each column flips half as often as the column to its right. Bit 1 flips every number, so bit 2 flips every 2 numbers, not every 4.
Q4
C — The rightmost column alternates every number. After 10 (1010) ending in 0, 11 (1011) must end in 1.
Q5
B — The smallest four-bit number is 0000, which is 0. The pattern 0001 is 1.