Binary number system in Intro to Computing - Draw & Build Visually

Draw This - beginner

Convert the decimal number 45 to its binary equivalent and draw the step-by-step division-by-2 process showing remainders.

5 minutes

Hint 1

Hint 2

Hint 3

Grading Criteria

Correct division steps shown with quotient and remainder

Remainders are only 0 or 1

Binary number formed by reading remainders bottom to top

Final binary number matches decimal 45 (101101)

Solution

Decimal to Binary Conversion of 45:

  45 ÷ 2 = 22 remainder 1
  22 ÷ 2 = 11 remainder 0
  11 ÷ 2 = 5  remainder 1
   5 ÷ 2 = 2  remainder 1
   2 ÷ 2 = 1  remainder 0
   1 ÷ 2 = 0  remainder 1

Binary number (read remainders bottom to top): 101101

To convert decimal 45 to binary, we divide by 2 repeatedly and note the remainders:

• 45 divided by 2 is 22 with remainder 1.
• 22 divided by 2 is 11 with remainder 0.
• 11 divided by 2 is 5 with remainder 1.
• 5 divided by 2 is 2 with remainder 1.
• 2 divided by 2 is 1 with remainder 0.
• 1 divided by 2 is 0 with remainder 1.

Reading the remainders from bottom to top gives the binary number: 101101.

Variations - 2 Challenges

[beginner] Convert the decimal number 13 to binary using the division-by-2 method and draw the step-by-step process.

[intermediate] Convert the decimal number 156 to binary using the division-by-2 method and draw the step-by-step process.