Writing small numbers in binary

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Writing small numbers in binary

Name:
Date:
Class:
A

Quick Questions

Shade in the A or B circle for each question.

1. To write 5 in binary using the place values 8, 4, 2, 1, which place values do you add?
A 4 and 1
B 8 and 2
2. Which is 5 written in binary?
A 0101
B 0110
3. In binary, what does a 0 under a place value mean?
A That place value is not added
B That place value is added twice
4. Which is 3 written in binary?
A 0101
B 0011
5. What is 8 written in binary using the place values 8, 4, 2, 1?
A 0001
B 1000
B

Match the Pairs

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

Left columnRight column
15 = 4 + 1 = 0101 AThe 1s are under the wrong place values. 9 uses 8 and 1, not 8 and 4. It should be 1001.
23 = 2 + 1 = 0011 BThe 1 under the 1 place is wrong. 6 does not use the 1 place value, so it needs a 0 there. It should be 0110.
3To write 8 in binary, you only need the 8 place value, so it gets a 1 and the others get 0 C8 = 1000
4To write 15 in binary, you add every place value, so every place gets a 1 DAdd the place values 2 and 1 to make 3, so write 1 under 2 and 1, and 0 under 8 and 4
56 = 4 + 2 = 0111 E15 = 8 + 4 + 2 + 1 = 1111
69 = 8 + 1 = 1100 FAdd the place values 4 and 1 to make 5, so write 1 under 4 and 1, and 0 under 8 and 2
C

Definitions

5 = 4 + 1 = 0101
D

Fill in the Blanks

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

1.
5 = 4 + 1 = ____
2.
Place values: 8, _, 2, 1
3.
6 = 4 + 2 = 0_10
4.
9 = 8 + 1 = ____
5.
3 = 2 + 1 = 00__
E

Spot the Error

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

Question 1
A Number: 6
B Add: 4 + 1 = 6
C Place values: 8 4 2 1
D Binary: 0110
Question 2
A Place values: 8 4 2 1
B Number: 3
C 3 = 4 + 1
D Binary: 0011
Question 3
A Place values: 8 6 4 2
B 7 = 4 + 2 + 1
C Binary: 0111
Question 4
A Number: 9
B 9 = 8 + 2
C Place values: 8 4 2 1
D Binary: 1001
Question 5
A Number: 10
B Place values: 8 4 2 1
C 10 = 8 + 2
D Binary: 1100

Answer Key

Writing small numbers in binary
Section A: Quick Questions
Q1
A — 4 and 1
Q2
A — 0101
Q3
A — That place value is not added
Q4
B — 0011
Q5
B — 1000
Section B: Match the Pairs
Q1
5 = 4 + 1 = 0101 → Add the place values 4 and 1 to make 5, so write 1 under 4 and 1, and 0 under 8 and 2
Q2
3 = 2 + 1 = 0011 → Add the place values 2 and 1 to make 3, so write 1 under 2 and 1, and 0 under 8 and 4
Q3
To write 8 in binary, you only need the 8 place value, so it gets a 1 and the others get 0 → 8 = 1000
Q4
To write 15 in binary, you add every place value, so every place gets a 1 → 15 = 8 + 4 + 2 + 1 = 1111
Q5
6 = 4 + 2 = 0111 → The 1 under the 1 place is wrong. 6 does not use the 1 place value, so it needs a 0 there. It should be 0110.
Q6
9 = 8 + 1 = 1100 → The 1s are under the wrong place values. 9 uses 8 and 1, not 8 and 4. It should be 1001.
Section C: Definitions
Q1
5 = 4 + 1 = 0101 — To write a number in binary, put a 1 under each place value you add and a 0 under the rest. Place values are 8, 4, 2, 1. So 5 is 4 + 1, which is 0101.
Section D: Fill in the Blanks
Q1
5 = 4 + 1 = 0101
Q2
Place values: 8, 4, 2, 1
Q3
6 = 4 + 2 = 0110
Q4
9 = 8 + 1 = 1001
Q5
3 = 2 + 1 = 0011
Section E: Spot the Error
Q1
B — 4 + 1 makes 5, not 6. To make 6 you add the place values 4 and 2, so the line should be Add: 4 + 2 = 6.
Q2
C — 4 + 1 is 5, not 3. The place values that add up to 3 are 2 and 1, so the line should be 3 = 2 + 1.
Q3
A — The four binary place values are 8, 4, 2 and 1. Each one is double the place value to its right. The line should be Place values: 8 4 2 1.
Q4
B — 8 + 2 makes 10, not 9. Nine is 8 + 1, so the line should be 9 = 8 + 1.
Q5
D — 10 = 8 + 2, so put a 1 under 8 and under 2, and a 0 under 4 and under 1. That gives Binary: 1010. The broken line has 1s under 8 and 4, which is 12.