Numbers and operations · Ages 13–14

Binary numbers worksheet

Part of: Laws of integral indices

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Numbers and operations · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.As a decimal number: 1111₂ =
Answer:
2.In binary: 14 = ₂
Answer:
3.1010₂ = 1 × 2³ + × 2² + × 2¹ + × 2⁰ =
Fill in each blank
Answer:
4.Divide by 2 again and again: 9 ÷ 2 = 4 r , 4 ÷ 2 = 2 r , 2 ÷ 2 = 1 r , 1 ÷ 2 = 0 r 1. So 9 = ₂
Fill in each blank
Answer:
5.In binary: 49 = ₂
Answer:
6.As a decimal number: 110001₂ =
Answer:
7.Divide by 2 again and again: 11 ÷ 2 = 5 r , 5 ÷ 2 = 2 r , 2 ÷ 2 = 1 r , 1 ÷ 2 = 0 r 1. So 11 = ₂
Fill in each blank
Answer:
8.In binary: 101₂ + 110₂ = ₂
Answer:
9.What is the largest 9-digit binary number, as a decimal number?
Answer:

13.Change 14 into binary by dividing by 2 again and again. Put the steps in order.
- A. 14 ÷ 2 = 7 r 0
- B. 7 ÷ 2 = 3 r 1
- C. 1 ÷ 2 = 0 r 1
- D. 3 ÷ 2 = 1 r 1
Write the letters in the right order
Working:
Answer:
14.Ka-yee says the binary number 111011₂ is even. Ka-yee is right.
True or false?
Working:
Answer:
15.11110₂ as a decimal number: 1 × 2⁴ + × 2³ + × 2² + × 2¹ + × 2⁰ =
Fill in each blank
Working:
Answer:
16.A machine shows two binary numbers, 1011₂ and 1011₂. What is their sum as a decimal number?
Working:
Answer:
17.Someone changes 1100₂ into a decimal number and gets 3. What is wrong? What is the right answer?
1. (1)From the left the place values are 1, 2, 4, 8
2. (2)Add the place values under the 1s
3. (3)That gives 3
Find the wrong step, then write the right answer
Working:
Answer:
18.A bit can only be 0 or 1. How many different numbers can 9 bits show?
Working:
Answer:

Show the answers and working

Binary numbers worksheet: Answers and working

1. 15
From the right the place values are 1, 2, 4, 8: add the place values under the 1s, 15.
2. 1110
Split 14 into 8, 4, 2 and 1, each once at most: 1 where one is used, 0 where not, 1110₂.
3. 0, 1, 0, 10
Each digit times its place value, 8, 4, 2 and 1 from the left, added: 10.
4. 1, 0, 0, 1001
Read the remainders from the bottom up: 1, 0, 0, 1. So 9 = 1001₂.
5. 110001
Divide by 2 again and again and read the remainders from the bottom up; or pick from 32, 16, 8, 4, 2, 1 those that add to 49: 110001₂.
6. 49
From the right the place values are 1, 2, 4, 8, 16, 32: add those under the 1s, 49.
7. 1, 1, 0, 1011
Read the remainders from the bottom up: 1, 0, 1, 1. So 11 = 1011₂.
8. 1011
As decimals first: 5 + 6 = 11, then back to binary: 1011₂. Or add digit by digit, where 1 + 1 = 10₂ carries.
9. 511
The largest has 9 1s; add 1 and it becomes 1 followed by 9 0s, 2⁹ = 512. So it is 512 − 1 = 511.

10. True
From the right the place values are 1, 2, 4, 8, so the leftmost is 8, not 1: 1011₂ = 11.
11. False
From the right the place values are 1, 2, 4, 8, so the leftmost is 8, not 1: 1100₂ = 12.
12. A. 1100₂
Split 12 into 8, 4, 2 and 1, each once at most, with 1 where one is used: 1100₂.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. A → B → D → C
Divide each quotient by 2 again until it is 0; read the remainders from the bottom up: 14 = 1110₂.
14. False
In binary every place value but the last is even, so look only at the last digit: 0 even, 1 odd.
15. 1, 1, 1, 0, 30
Each digit times its place value, 16, 8, 4, 2 and 1 from the left, added: 30.
16. 22
1011₂ = 11 and 1011₂ = 11, so the sum is 11 + 11 = 22.
17. 12
Place values run from the right: 1, 2, 4, 8, so the leftmost is 8 and 1100₂ = 12.
18. 512 numbers
Each bit has 2 choices, so 9 bits give 2⁹ = 512 different patterns.

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