AP CSP Practice: Binary to Decimal Conversion

Big Idea 2: Data
Day 2 Practice • AP CSP Daily Question
🎯 Focus: Binary and Data Representation

Practice Question

What is the decimal (base 10) equivalent of the binary number 10110?
What This Tests: Big Idea 2 covers data representation, including how binary (base 2) numbers can be converted to decimal (base 10).

Step-by-Step Solution

To convert binary to decimal, multiply each digit by its place value (powers of 2) and add them together.

Position 4 3 2 1 0
Place Value 2⁴ = 16 2³ = 8 2² = 4 2¹ = 2 2⁰ = 1
Binary Digit 1 0 1 1 0
Value 16 0 4 2 0

16 + 0 + 4 + 2 + 0 = 22

The Quick Method

Write out the place values from right to left: 1, 2, 4, 8, 16, 32...

Then add only the values where there's a 1:

Binary:  1    0    1    1    0
         ↓    ↓    ↓    ↓    ↓
Values: 16    8    4    2    1
        ↓         ↓    ↓
        16   +    4  + 2  = 22

Common Mistakes

Mistake: Reading binary as decimal

10110 is NOT "ten thousand one hundred ten." Each digit represents a power of 2, not a power of 10.

Mistake: Starting place values from wrong end

Place values start from the RIGHT (2⁰ = 1), not the left. The rightmost digit is always the 1s place.

💡 AP Exam Tip

Memorize the first 8 powers of 2: 1, 2, 4, 8, 16, 32, 64, 128. This makes binary conversion much faster on the exam!

Difficulty: Easy • Time: 1-2 minutes • Topic: 2.1 Binary Numbers

Want More AP CSP Practice?

Get personalized help from an experienced AP CS teacher

AP CSP Study Guide Schedule 1-on-1 Tutoring
Back to blog