CS: Binary: Counting with 0s and 1s
Learn how computers count using only two digits
CS: Binary: Counting with 0s and 1s
Learn how computers count using only two digits
CS - Grade 4-5
- 1
Binary uses only two digits: 0 and 1. Write the binary numbers for decimal numbers 0, 1, 2, and 3.
Think about how counting moves to a new place after you run out of digits.
The binary numbers are 0, 1, 10, and 11. In binary, after 1 comes 10 because there are only two digits to use. - 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?
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. - 3
Write the decimal number 6 in binary using the place values 4, 2, and 1.
Choose place values that add up to 6.
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. - 4
What decimal number does the binary number 1001 represent? Use the place values 8, 4, 2, and 1.
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. - 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?
Add the values of the switches that are on.
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. - 6
Complete this counting pattern in binary: 0, 1, 10, 11, __, __.
The missing binary numbers are 100 and 101. The pattern is counting in binary from 0 to 5. - 7
Circle the larger binary number: 10 or 11. Explain how you know.
Convert each binary number to decimal before comparing.
The larger binary number is 11. The binary number 10 equals 2 in decimal, and 11 equals 3 in decimal. - 8
Explain why computers can use binary to store information.
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. - 9
In the binary number 110, which place values are turned on? Use the place values 4, 2, and 1.
A 1 means the place value is used, and a 0 means it is not used.
In 110, the 4 and 2 place values are turned on. The 1 place is turned off, so the number equals 4 + 2 = 6. - 10
Write the decimal number 13 in binary using the place values 8, 4, 2, and 1.
Find which of 8, 4, 2, and 1 add up to 13.
The decimal number 13 is 1101 in binary. The 8, 4, and 1 places are turned on because 8 + 4 + 1 = 13. - 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?
The code 11 belongs to Group C. The list shows that Group C is matched with the binary code 11. - 12
What binary number comes right after 101 when counting?
Convert 101 to decimal, add 1, then convert back to binary.
The binary number that comes right after 101 is 110. This is like saying that 5 comes before 6 in decimal counting. - 13
Fill in the missing number in this binary counting sequence: 1, 10, 11, 100, __, 110.
The missing binary number is 101. The sequence is counting in binary from 1 to 6. - 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?
Use the largest cards first, then see what is still needed.
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. - 15
Sam says the binary number 100 equals 1 because 1 + 0 + 0 = 1. Explain Sam's mistake and give the correct decimal number.
The position of each digit matters in binary.
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.