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

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Quick Questions

Shade in the A or B circle for each question.

1. What is 8 written in binary?

A 0111

B 1000

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

3. Which binary number is 15?

A 1111

B 1110

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

5. Which is the largest number you can show with 4 bits?

A 15 (1111)

B 16 (10000)

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
11000		A1101
21111		BThe number 15 in binary, the largest number that fits in 4 bits.
3Counting from 8 to 15 repeats the 0 to 7 pattern with a leading 1 in front. So 5 (101) becomes 13.		C10000 is 16, not 15. The largest 4-bit number is 1111, which is 15.
4After 7 (111) the three bits run out, so a new column is added to the left to write 8.		D111 -> 1000
58 = 111		E111 is 7, not 8. Three bits can only count up to 7, so 8 needs a fourth bit and is written 1000.
615 = 10000		FThe number 8 in binary. A fourth bit is needed, so a new column is added with a 1 in it.

Definitions

1000 to 1111

Fill in the Blanks

Complete each line of code by filling in the missing parts.

7 = 0111 8 = ____ 9 = 1001

Largest 4-bit number: ____ = 15

1010 is 10, 1011 is __, 1100 is 12

7 needs 3 bits, but 8 needs _ bits

1 = 0001 9 = 1___

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A 8 = 0111

B 9 = 1001

C 10 = 1010

Question 2

A 11 = 1011

B 12 = 1100

C 13 = 1110

Question 3

A Count in binary: 8 to 15

B 14 = 1101

C 15 = 1111

Question 4

A 8 = 1000

B 9 = 1001

C 10 = 1010

D 11 = 1100

Question 5

A bits = 4

B largest = 1111

C denary = 16

Answer Key

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

Section A: Quick Questions

B — 1000

A — Three bits can only show 0 to 7, so 8 needs a new column

A — 1111

B — They all start with a 1 in the 8s place

A — 15 (1111)

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

7 = 0111
8 = 1000
9 = 1001

Largest 4-bit number: 1111 = 15

1010 is 10, 1011 is 11, 1100 is 12

7 needs 3 bits, but 8 needs 4 bits

1 = 0001
9 = 1001

Section E: Spot the Error

A — 0111 is 7. Counting past 7 needs a fourth bit, so 8 is written 1000.

C — 1110 is 14, not 13. After 1100 (12) the next number is 1101, which is 13.

B — 1101 is 13. 14 is 1110, the number just before 1111.

D — 1100 is 12. 11 is 1011, one more than 1010 (10).

C — 1111 is the largest 4-bit number and it equals 15 in denary, not 16.