Activity 01
Relay Race: Decimal to Binary Conversions
Divide class into small groups and line them up. Call a decimal number; first student writes its binary on the board, next verifies by converting back to decimal, then tags the following student. Continue for 10 numbers, with fastest accurate team winning. Debrief conversions as a class.
Explain why computers use a binary system instead of a decimal system.
Facilitation TipDuring the Relay Race, have students physically flip switches to show each bit change, reinforcing the connection between binary digits and circuit states.
What to look forPresent students with a binary number, such as 10110. Ask them to write the decimal equivalent on a mini-whiteboard and hold it up. Then, give them a decimal number, like 21, and ask them to write its 8-bit binary representation.
RememberUnderstandApplyAnalyzeSelf-ManagementRelationship Skills
Generate Complete Lesson→· · ·
Activity 02
Bead Strings: Binary Place Values
Provide beads on strings marked with powers of 2 (1, 2, 4, 8, etc.). Pairs create binary strings for given decimals, then trade to decode partner's number. Extend by limiting to 5 beads to show overflow. Discuss patterns observed.
Construct the binary representation of small decimal numbers.
Facilitation TipHave students create bead strings with two colors to physically represent place values, making the concept of powers of 2 tangible.
What to look forPose the question: 'Imagine you have only 4 bits to represent a number. What is the largest decimal number you can represent? What happens if you try to represent a number larger than that?' Facilitate a class discussion on the concept of overflow.
RememberUnderstandApplyAnalyzeSelf-ManagementRelationship Skills
Generate Complete Lesson→· · ·
Activity 03
Overflow Simulator: Fixed-Bit Addition
Small groups use cards labeled 0-1 for 8 bits. Add two binary numbers on paper first, then simulate with cards, noting overflow when a 9th bit appears. Rotate roles for recording results. Class shares overflow examples.
Analyze the limitations of representing numbers with a fixed number of bits.
Facilitation TipUse the Overflow Simulator to let students adjust bit length and observe how numbers wrap or indicate overflow, creating a shared visual reference.
What to look forAsk students to write down two reasons why computers use binary instead of the decimal system. Additionally, have them convert the binary number 1101 to its decimal equivalent.
RememberUnderstandApplyAnalyzeSelf-ManagementRelationship Skills
Generate Complete Lesson→· · ·
Activity 04
Binary Bingo: Recognition Game
Whole class gets bingo cards with binary numbers. Call decimals; students mark matching binaries and verify with neighbors. First bingo leads a group teach-back on their winning conversion. Adapt for larger numbers.
Explain why computers use a binary system instead of a decimal system.
Facilitation TipPlay Binary Bingo with cards that include both binary and decimal numbers, requiring students to convert during the game to strengthen recognition and recall.
What to look forPresent students with a binary number, such as 10110. Ask them to write the decimal equivalent on a mini-whiteboard and hold it up. Then, give them a decimal number, like 21, and ask them to write its 8-bit binary representation.
RememberUnderstandApplyAnalyzeSelf-ManagementRelationship Skills
Generate Complete Lesson→A few notes on teaching this unit
Start with the Bead Strings activity to build place value understanding, then use the Relay Race to practice conversions under time pressure. Research shows that timed drills improve automaticity, but only after conceptual grounding. Avoid rushing to algorithms before students can explain why each bit represents a power of 2. Use the Overflow Simulator to confront limits immediately, linking binary math to real hardware constraints.
Students will explain why computers use binary instead of decimal, convert small decimals to 8-bit binary, and identify overflow limits in fixed-bit systems. They will justify their answers using place value and circuit behavior.
Watch Out for These Misconceptions
During the Relay Race, watch for students who treat binary as a longer decimal version without recognizing its hardware purpose.
Pause the race after each set and ask teams to explain why computers use two states. Have them point to the relays in their setup and link each 0 or 1 to low or high voltage.
During the Overflow Simulator, watch for students who assume any number can fit into 8 bits without limits.
Have students set the simulator to 8 bits, input 256, and observe the overflow warning. Then ask them to calculate 255+1 and explain where the extra bit would go.
During the Binary Bingo game, watch for students who think computers still convert everything to decimal inside.
After the game, ask students to trace a number from their card: human decimal input, binary conversion for the machine, and back to decimal for the human output. Have peers verify each step.
Methods used in this brief