Reading binary numbers

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Quick Questions

Shade in the A or B circle for each question.

1. To read the binary number 101, which place values do you add?

A 4 + 1 = 5, because the 1s are under 4 and 1

B 1 + 0 + 1 = 2, because you just count the digits

2. What is 1011 in decimal?

A 11

B 13

3. What do you do with a place value that has a 0 under it?

A Add it twice

B Ignore it and do not add it

4. Which is the right way to read 1100?

A 8 + 4 = 12

B 2 + 1 = 3

5. Do leading zeros change the value of a binary number? Look at 0011 and 11.

A Yes, 0011 is bigger than 11

B No, both are 3 because the zeros add nothing

Match the Pairs

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

Left column		Right column
11011 = 8 + 2 + 1 = 11		A8 + 1 = 9
20101 = 5		BThe place values were counted as 1, 2, 3 instead of 1, 2, 4, 8. Only 2 + 1 should be added, so the answer is 3.
3Write 110 as a decimal number by adding the place values that have a 1		C4 + 2 = 6
4Check your answer: the binary number 1001 should add up to 9		DAdd the place values that have a 1 (8, 2 and 1) and ignore the 0 to get the decimal number 11
51010 = 8 + 2 + 1 + 0 = 11		EThe 1 place value was added even though it has a 0 under it. Only add place values that have a 1. The correct answer is 8 + 2 = 10.
60011 = 1 + 2 + 3 = 6		FLeading zeros do not change the value, so 0101 is the same number as 101

Definitions

Add the place values that have a 1

Fill in the Blanks

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

1011 = 8 + 2 + _ = 11

0101 has the same value as ___

Place values: 8, 4, _, 1

1101 = 8 + 4 + 1 = __

A _ means add the place value above it

Spot the Error

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

Question 1

A Binary: 101

B Place values: 5 3 1

C Add 4 + 1

D Decimal: 5

Question 2

A Binary: 1101

B Place values: 8 4 2 1

C Add 8 + 4 + 1

D Decimal: 14

Question 3

A Binary: 110

B Place values: 4 2 1

C Add 4 + 2 + 1

D Decimal: 6

Question 4

A Binary: 1001

B Add 8 + 2 + 1

C Answer: 9

Question 5

A Binary: 111

B Place values: 4 2 1

C Add 4 + 2 + 1 = 7

D Check: 3 bits is at most 8

Answer Key

Reading binary numbers

Section A: Quick Questions

A — 4 + 1 = 5, because the 1s are under 4 and 1

A — 11

B — Ignore it and do not add it

A — 8 + 4 = 12

B — No, both are 3 because the zeros add nothing

Section B: Match the Pairs

1011 = 8 + 2 + 1 = 11 → Add the place values that have a 1 (8, 2 and 1) and ignore the 0 to get the decimal number 11

0101 = 5 → Leading zeros do not change the value, so 0101 is the same number as 101

Write 110 as a decimal number by adding the place values that have a 1 → 4 + 2 = 6

Check your answer: the binary number 1001 should add up to 9 → 8 + 1 = 9

1010 = 8 + 2 + 1 + 0 = 11 → The 1 place value was added even though it has a 0 under it. Only add place values that have a 1. The correct answer is 8 + 2 = 10.

0011 = 1 + 2 + 3 = 6 → The place values were counted as 1, 2, 3 instead of 1, 2, 4, 8. Only 2 + 1 should be added, so the answer is 3.

Section C: Definitions

Add the place values that have a 1 — To read a binary number, add up the place values (1, 2, 4, 8...) that have a 1 under them and ignore the 0s. For example, 1011 is 8 + 2 + 1 = 11.

Section D: Fill in the Blanks

1011 = 8 + 2 + 1 = 11

0101 has the same value as 101

Place values: 8, 4, 2, 1

1101 = 8 + 4 + 1 = 13

A 1 means add the place value above it

Section E: Spot the Error

B — Binary place values double each time, starting at 1. For three digits they are 4, 2, 1, not 5, 3, 1.

D — The 1s are under 8, 4 and 1. 8 + 4 + 1 = 13, so the decimal answer is 13, not 14.

C — The last digit is 0, so the place value 1 is ignored. Only add 4 + 2.

B — Only the place values with a 1 are added. 1001 has 1s under 8 and 1, so the sum is 8 + 1. The 2 has a 0 under it.

D — With 3 bits the biggest number is 4 + 2 + 1 = 7. The answer must be 7 or less, so the check should say 7.