Binary CS Thinking Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

medium
Convert the decimal number 45 to binary.

Solution

  1. 1
    Step 1: 45 ÷ 2 = 22 remainder 1.
  2. 2
    Step 2: 22 ÷ 2 = 11 r0. 11 ÷ 2 = 5 r1. 5 ÷ 2 = 2 r1. 2 ÷ 2 = 1 r0. 1 ÷ 2 = 0 r1.
  3. 3
    Step 3: Read remainders bottom to top: 101101.

Answer

1011012101101_2
Binary (base 2) uses only digits 0 and 1. Repeatedly dividing by 2 and collecting remainders converts decimal to binary. Computers use binary because electronic circuits have two states: on and off.

About Binary

Binary is a base-2 number system that uses only two digits, 0 and 1, to represent all values. Each digit position represents a power of 2, and computers use binary because electronic circuits have exactly two states: on and off.

Learn more about Binary →

More Binary Examples

Example 2 medium

Convert binary [formula] to decimal.

Example 3 medium

Add the binary numbers [formula] and [formula].

Example 4 medium

Convert the decimal number 13 to binary using powers of 2.

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