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Counting in binary from 8 to 15 (Binary Number Representation)

Binary for 8 to 15. Counting past 7 needs a fourth bit, so 8 is 1000 and the numbers keep a leading 1 up to 1111, which is 15, the largest 4-bit number.

Part of: ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 8

Understanding Counting in binary from 8 to 15 (Binary Number Representation) in ACARA Digital Technologies Years 7–8

What it does: 13 is 8 + 5. Put a 1 in the new fourth column and add the pattern for 5, which is 101, to get 1101. Adding 1 to 111 makes every bit roll over to 0 and a new leading 1 appears. This gives 1000, which is 8. After 111 (7) all three bits are full, so we add a fourth column. 8 is 1000, with a 1 in the 8s place. 1111 = 8 + 4 + 2 + 1 = 15. 1110 is 14. With four bits, the biggest number is 1111, which is 15. 16 needs a fifth bit.

Common mistakes: 0111 is 7. Counting past 7 needs a fourth bit, so 8 is written 1000. 1110 is 14, not 13. After 1100 (12) the next number is 1101, which is 13.

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This module's key terms are also in a printable crossword (Modules 173–188) and word search (Modules 153–188).

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Learning
Duo
What is 8 written in binary?
10000111
Matches
8 = 111
↓
111 is 7, not 8. Three bits can only count up to 7, so 8 needs a fourth bit and is written 1000.
Applying
Meanings
Term
1000 to 1111
Meaning
Binary for 8 to 15. Counting past 7 needs a fourth bit, so 8 is 1000 and the numbers keep a leading 1 up to 1111, which is 15, the largest 4-bit number.
Practice
8 = 1000
Testing
Gaps
8 =
Check Answer
Spots
18 = 0111
29 = 1001

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Quick Questions

1. What is 8 written in binary?
A. 0111
B. 1000 ✓
After 111 (7) all three bits are full, so we add a fourth column. 8 is 1000, with a 1 in the 8s place.
2. Why do we need a fourth bit to count past 7?
A. Three bits can only show 0 to 7, so 8 needs a new column ✓
B. Three bits can only show 0 to 3, so 4 needs a new column
Three bits give 8 values, from 0 to 7. The next number, 8, needs a fourth bit.
3. Which binary number is 15?
A. 1111 ✓
B. 1110
1111 = 8 + 4 + 2 + 1 = 15. 1110 is 14.
4. What do the binary numbers for 8 to 15 all have in common?
A. They all start with a 0 in the 8s place
B. They all start with a 1 in the 8s place ✓
1000 to 1111 all have a leading 1. The last three bits repeat the pattern from 0 to 7.
5. Which is the largest number you can show with 4 bits?
A. 15 (1111) ✓
B. 16 (10000)
With four bits, the biggest number is 1111, which is 15. 16 needs a fifth bit.

Match the Pairs

1000 → The number 8 in binary. A fourth bit is needed, so a new column is added with a 1 in it.
1111 → The number 15 in binary, the largest number that fits in 4 bits.
Counting from 8 to 15 repeats the 0 to 7 pattern with a leading 1 in front. So 5 (101) becomes 13. → 1101
After 7 (111) the three bits run out, so a new column is added to the left to write 8. → 111 -> 1000
8 = 111 → 111 is 7, not 8. Three bits can only count up to 7, so 8 needs a fourth bit and is written 1000.
15 = 10000 → 10000 is 16, not 15. The largest 4-bit number is 1111, which is 15.

Key Term

1000 to 1111
Binary for 8 to 15. Counting past 7 needs a fourth bit, so 8 is 1000 and the numbers keep a leading 1 up to 1111, which is 15, the largest 4-bit number.

Fill in the Blanks

1. 7 = 0111 8 = 1000 9 = 1001
Hint: Type the 4-bit binary number for 8. It is the first number that needs a fourth column.
2. Largest 4-bit number: 1111 = 15
Hint: Type the binary number with all four bits switched on.
3. 1010 is 10, 1011 is 11, 1100 is 12
Hint: Type the denary number that comes between 10 and 12.
4. 7 needs 3 bits, but 8 needs 4 bits
Hint: Type how many bits are needed once counting passes 7.
5. 1 = 0001 9 = 1001
Hint: After the leading 1, the last three bits repeat the pattern used for the number 1.

Spot the Error

Question 1
A 8 = 0111
B 9 = 1001
C 10 = 1010
Line A — 0111 is 7. Counting past 7 needs a fourth bit, so 8 is written 1000.
Question 2
A 11 = 1011
B 12 = 1100
C 13 = 1110
Line C — 1110 is 14, not 13. After 1100 (12) the next number is 1101, which is 13.
Question 3
A Count in binary: 8 to 15
B 14 = 1101
C 15 = 1111
Line B — 1101 is 13. 14 is 1110, the number just before 1111.
Question 4
A 8 = 1000
B 9 = 1001
C 10 = 1010
D 11 = 1100
Line D — 1100 is 12. 11 is 1011, one more than 1010 (10).
Question 5
A bits = 4
B largest = 1111
C denary = 16
Line C — 1111 is the largest 4-bit number and it equals 15 in denary, not 16.

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