CS: Binary: Counting with 0s and 1s Worksheet

Question 1

Binary uses only two digits: 0 and 1. Write the binary numbers for decimal numbers 0, 1, 2, and 3.

Accepted Answer

The binary numbers are 0, 1, 10, and 11. In binary, after 1 comes 10 because there are only two digits to use.

Question 2

A binary number has place values. In 101, the places from left to right are 4, 2, and 1. What decimal number is 101?

Accepted Answer

The binary number 101 equals 5 in decimal. The 1 in the 4s place counts as 4, the 0 in the 2s place counts as 0, and the 1 in the 1s place counts as 1, so 4 + 1 = 5.

Question 3

Write the decimal number 6 in binary using the place values 4, 2, and 1.

Accepted Answer

The decimal number 6 is 110 in binary. The 4 and 2 places are turned on, and the 1 place is turned off, so 4 + 2 = 6.

Question 4

What decimal number does the binary number 1001 represent? Use the place values 8, 4, 2, and 1.

Accepted Answer

The binary number 1001 represents 9 in decimal. The 8 place is on, the 4 and 2 places are off, and the 1 place is on, so 8 + 1 = 9.

Question 5

Two switches have values of 2 and 1. A switch that is on means 1, and a switch that is off means 0. If both switches are on, what is the binary number and what decimal number does it represent?

Accepted Answer

The binary number is 11, and it represents 3 in decimal. Both switches are on, so the values 2 and 1 are added together to make 3.

Question 6

Complete this counting pattern in binary: 0, 1, 10, 11, __, __.

Accepted Answer

The missing binary numbers are 100 and 101. The pattern is counting in binary from 0 to 5.

Question 7

Circle the larger binary number: 10 or 11. Explain how you know.

Accepted Answer

The larger binary number is 11. The binary number 10 equals 2 in decimal, and 11 equals 3 in decimal.

Question 8

Explain why computers can use binary to store information.

Accepted Answer

Computers can use binary because many computer parts have two states, such as on and off. The digit 1 can represent on, and the digit 0 can represent off.

Question 9

In the binary number 110, which place values are turned on? Use the place values 4, 2, and 1.

Accepted Answer

In 110, the 4 and 2 place values are turned on. The 1 place is turned off, so the number equals 4 + 2 = 6.

Question 10

Write the decimal number 13 in binary using the place values 8, 4, 2, and 1.

Accepted Answer

The decimal number 13 is 1101 in binary. The 8, 4, and 1 places are turned on because 8 + 4 + 1 = 13.

Question 11

A class uses binary codes for four groups: Group A = 1, Group B = 10, Group C = 11, and Group D = 100. Which group has the code 11?

Accepted Answer

The code 11 belongs to Group C. The list shows that Group C is matched with the binary code 11.

Question 12

What binary number comes right after 101 when counting?

Accepted Answer

The binary number that comes right after 101 is 110. This is like saying that 5 comes before 6 in decimal counting.

Question 13

Fill in the missing number in this binary counting sequence: 1, 10, 11, 100, __, 110.

Accepted Answer

The missing binary number is 101. The sequence is counting in binary from 1 to 6.

Question 14

You have four binary cards with values 8, 4, 2, and 1. Which cards should be turned on to make the decimal number 14, and what is 14 in binary?

Accepted Answer

The 8, 4, and 2 cards should be turned on, and the 1 card should be turned off. The decimal number 14 is 1110 in binary because 8 + 4 + 2 = 14.

Question 15

Sam says the binary number 100 equals 1 because 1 + 0 + 0 = 1. Explain Sam's mistake and give the correct decimal number.

Accepted Answer

Sam's mistake is adding the digits instead of using place values. In binary 100, the 1 is in the 4s place, so 100 equals 4 in decimal.

CS: Binary: Counting with 0s and 1s

More CS Worksheets

More Grade 4-5 Worksheets