What are binary numbers?

Lesson Content

• Lesson Plan Template:

  CTE Lesson Plan

• CTE Course Info and Benchmark Notes

  
  

  Program Title (as applicable): N/A

  Course Title: Coding Fundamentals

  Course Number: 9009200

  Career Cluster: Information Technology

  CIP Number: 0511020109

  Course Type: Orientation/Exploratory

  Standard(s) or benchmarks

  Focus:

  • 02.03 Examine connections between elements of mathematics and computer science including binary numbers, logic, sets, and functions.
  • SC.68.CS-CS.1.1 Examine connections between elements of mathematics and computer science including binary numbers, logic, sets, and functions.

  Supporting:

  • MA.6.NSO.4.1 Apply and extend previous understandings of operations with whole numbers to add and subtract integers with procedural fluency.
  • MA.6.NSO.4.2 Apply and extend previous understandings of operations with whole numbers to multiply and divide integers with procedural fluency

• Unit Outline

  
  

  This is an introduction to binary numbers and can be used to teach a foundational understanding of the composition of binary numbers and how to read them. This lesson can be used at the beginning of a unit focused on binary numbers and their relation to computers or computer programming.

• Career Connection

  
  

  By grappling with and making sense of the equations containing binary and base ten values, students will sharpen their problem solving skills while drawing connections between binary and base ten values. Developing an understanding of binary numbers will help students explore computer science concepts and topics that are commonly used in the career field.

• Learning Objectives

  
  

  Students will be able to:

  • Decode binary numbers
  • Compare and contrast binary and base ten numbers
  • Explain the relevance of binary numbers

• Prior Knowledge

  
  

  Students should be familiar with:

  • Identifying place value
  • Adding and multiplying values

• Guiding Questions

  
  
  • Why are binary numbers useful in computer science?
  • What are the benefits and drawbacks of using binary numbers?

• Procedure

  
  

  1. To introduce the lesson, display the Equation String PowerPoint. Ask students to examine the equation 10 + 11 = 5 and figure out how this can be true.

  • At a minimum, the second equation 10 + 100 = 6 should be shown to give students additional values to consider and to see if their ideas for the binary values hold true. Each equation will appear after clicking the mouse.
  • It is not intended for students to “decode” the binary numbers yet. Rather, they should use trial and error and provide reasoning for their ideas as to what values the binary numbers represent.

  2. Facilitate a discussion to probe students’ thinking. The following questions can be used:

  • What do you notice and wonder?
  • What do you think the values represent?
  • How did you determine what the values represent?
  • Why would someone use a code like this to represent numbers?
  • How do you think this type of number representation can be used?

  Use the last question as a segue to explain that the combinations of 0’s and 1’s represent binary numbers which are used in computer science. Emphasize the pre-fix bi means 2. Since computers are limited in logic and capacity, they interpret pieces of data in 2 states – true or false. 0’s represent a “false” state and 1’s represent an “true” state. Representing data using only 2 values lessens the demand on computers since they're interpreting a series of two numbers. The order of the numbers tells the computer the value it represents. Binary is very similar to a code used to communicate with computers.

  3. Put students in small groups of no more than 4. Pass out a copy of the Decoding Binary Numbers handout to each student.

  • Allow groups time to decode each equation. Let students know that it is okay if they don’t decode all the equations, but they should try to decode as many as they can.
  • While groups are collaborating, visit each group to monitor progress, address misconceptions, and answer questions, as needed.
  • Allow groups to share the equations they were able to decode and explain their reasoning to the class. If any equations were not decoded, the teacher can share those values so that students have all the equations decoded.

  4. Remind groups that binary numbers operate within a two-digit system. Facilitate a discussion to support students making connections between binary and base ten. The following questions can be used to guide discussion:

  • How many digits are used in base ten, our counting system?
  • How is base ten related to place value?

  i. Be sure to discuss how the placement of numbers in relation to the decimal point helps determine the value of numbers in base ten.

  ii. Be sure to discuss how there are 10 digits used (0 – 9) to create all numbers in a base ten system.

  • How many digits are used in binary?

  i. Be sure to explain the position in a binary integer is called a bit. Bits are units of data within the binary unit of information. The position of bits in binary numbers is similar to place value in base ten numbers.

  • How might we be able to use the order, or place value, of the binary numbers to figure out the value of each bit?
  • Allow students time to determine how the position of a bit in a binary number is related to its value.

  5. To close the lesson, have students share how they determined the relationship between the position of a bit and its numerical value.

  • Summarize that binary numbers are based on a base 2 system. The bit farthest to the right represents the least significant bit and every other bit moving to the left is one higher bit based on a power of 2.
  • Since students may not be familiar with powers, it can be explained as increasing the multiplication of 2 one time each time you “move” to the left in a binary number. The image can be used to help support students’ understanding.

• Teacher Notes

  
  
  • If time allows, students can provide a written response to one or both of the guiding questions to close the lesson.

• Optional

  
  

  Accommodation Suggestions:

  • The Decoding Binary Numbers V2 handout can be used to support students who may need additional support decoding the equations. Students use the 1st equation to determine 10 in binary is equivalent to 2 in base ten. Then, they are able to use that information to decode the rest of the equations.