Binary CS Thinking Example 4

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

Example 4

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

Solution

  1. 1
    Step 1: The largest powers of 2 that fit into 13 are 8, 4, and 1, because 13 = 8 + 4 + 1.
  2. 2
    Step 2: That means the 8s, 4s, 2s, and 1s places are 1, 1, 0, 1 respectively, so the binary number is 1101.

Answer

110121101_2
Binary represents numbers using powers of 2 instead of powers of 10. Writing which powers of 2 are present gives the binary form directly.

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 1 medium

Convert the decimal number 45 to binary.

Example 2 medium

Convert binary [formula] to decimal.

Example 3 medium

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

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