Ever wondered how computers understand everything? They use a secret language made of just two symbols: 0s and 1s! This is called binary code. In this quiz, you'll become a pro at translating these binary messages into numbers we understand every day (called decimal or denary numbers).
This is a super important skill in Computer Science, helping you understand how data is stored, processed, and transmitted inside any digital device, from your smartphone to a supercomputer!
Ready to Ace It? Here’s How:
Understand the Basics: Remember that each '1' or '0' in binary sits in a 'place' that has a specific value (like 1, 2, 4, 8, 16, and so on, doubling each time as you move left).
Look at the Example: We've got a step-by-step example on the next page that shows you exactly how to break down binary numbers.
Take Your Time: Don't rush! Work out the answer carefully on paper first, just like solving a puzzle.
Check Your Work: After you get the feedback, read the full explanation to see where you can improve.
Let's Learn How to Convert Binary!
Before you dive into the quiz, let's go through a step-by-step example. This will help you understand the trick to changing binary numbers into decimal numbers.
Example Question: Convert the binary number 10110101 to decimal.
Walkthrough:
Think of each digit in a binary number as a special "switch" that is either ON (1) or OFF (0). Each switch is connected to a light bulb, and each light bulb has a unique value.
Identify Place Values:
Starting from the rightmost digit (the very end of the binary number), each position has a specific value that doubles as you move left:
Rightmost digit: 1s place (which is 2 to the power of 0, or 20)
Second from right: 2s place (2 to the power of 1, or 21)
Third from right: 4s place (2 to the power of 2, or 22)
And so on... 8s place, 16s place, 32s place, 64s place, and for an 8-digit binary number, the leftmost is the 128s place (2 to the power of 7, or 27).
Match Binary Digits to Place Values:
For each position in the binary number, look at the digit ('1' or '0') and its place value:
For our example, 10110101:
The first '1' on the far left (8th digit) is at the 128s place. So, 1 × 128 = 128.
The '0' (7th digit) is at the 64s place. So, 0 × 64 = 0.
The '1' (6th digit) is at the 32s place. So, 1 × 32 = 32.
The '1' (5th digit) is at the 16s place. So, 1 × 16 = 16.
The '0' (4th digit) is at the 8s place. So, 0 × 8 = 0.
The '1' (3rd digit) is at the 4s place. So, 1 × 4 = 4.
The '0' (2nd digit) is at the 2s place. So, 0 × 2 = 0.
The '1' on the far right (1st digit) is at the 1s place. So, 1 × 1 = 1.
Add the "ON" Values:
Finally, add up all the values from the positions where the binary digit was a '1' (the "ON" switches):
128 + 0 + 32 + 16 + 0 + 4 + 0 + 1 = 181.
So, 10110101 in binary is 181 in decimal!
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Scenario: You are helping a robotics team debug their sensor data, which comes in 8-bit binary numbers. You need to quickly convert these values to decimal to analyse performance.