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Created on July 22, 2024 By red-rewards.com

Computer Science

Binary + Decimal Numbers

Can you convert binary numbers to decimal (normal) numbers and vice versa?
Tip: When converting decimal numbers to binary, use as few bits as possible
(Example: 5 = 101; NOT 0101, 00101 ….)

1 / 10

What is 100110 in decimal?

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2 / 10

What is 11101 in decimal?

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3 / 10

What is 47 in binary?

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4 / 10

What is 51 in binary?

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5 / 10

What is 54 in binary?

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6 / 10

What is 111000 in decimal?

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7 / 10

What is 11010 in decimal?

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8 / 10

What is 23 in binary?

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9 / 10

What is 21 in binary?

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10 / 10

What is 48 in binary?

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Useful Powers of 2

Quiz Guide

To help you with this quiz, I’ve created a guide explaining binary numbers.

First of all, what are decimal numbers?

Decimal numbers are the regular numbers we use on a day to day basis. Each position in a decimal number can be one of ten different digits, those being {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
When you see the number “123”, it doesn’t represent 1 + 2 + 3 or 1 * 2 * 3, rather it means:

1 * 10² + 2 * 10¹ + 3 * 10⁰

Which in words means one-hundred and twenty three. While this might seem basic, it’s key to understanding how binary numbers work.

What are binary numbers

Binary numbers are numbers that can be represented by one of two digits, those being 0 or 1.
When you see the number “1011”, it means:

1 * 2³ + 0 * 2² + 1 * 2¹ + 1 *2⁰

You end up with the following sum:

8 + 0 + 2 + 1 = 11

Unlike decimal numbers, where each digit represents a power of ten, each digit in a binary number represents a power of two. The far-right digit representing the smallest power of two, that being 2⁰ = 1. In the example above, the far-left digit represents the largest power of two, in this case being 2³ = 8.

As you’ve already seen, I’ve left a table of powers of 2 to help you with the quiz

Conversion examples

Now that we know the basics, let’s try converting some decimal numbers into binary and vice versa. For my examples, I’ll be using numbers smaller than 64, just like the questions in the quiz.

Convert 42 into binary

To start, let’s find out the largest power of 2, that is smaller than our number. According to our table of powers of 2 above, the largest one, that is still smaller than 42, would be 2⁵, which is 32. Our number will look something like this:

1 * 2⁵ + X * 2⁴ + X * 2³ + X * 2² + X * 2¹ + X *2⁰

We’ll now subtract 32 from 42. 42 – 32 is 10. Now we need to go through the powers of two smaller than 2⁵ and see if they’re smaller than 10.

Is 2⁴ = 16 smaller than 10? Nope. Our number will look something like this:

1 * 2⁵ + 0 * 2⁴ + X * 2³ + X * 2² + X * 2¹ + X *2⁰

The next power of two is 2³ = 8. Is that smaller than 10? Yes it is! Our number will look something like this:

1 * 2⁵ + 0 * 2⁴ + 1 * 2³ + X * 2² + X * 2¹ + X *2⁰

We’ll now subtract 8 from 10. 10 – 8 is 2.

Since 2 is 2¹, we know that that position in the number has to be 1, whilst the position for 2² has to be 0. And since 2 – 2 = 0, there are no longer any powers of 2 smaller than 0, hence we have our binary number, which is:

1 * 2⁵ + 0 * 2⁴ + 1 * 2³ + 0 * 2² + 1 * 2¹ + 0 *2⁰ = 101010

We can double check whether the number is correct:

32 + 0 + 8 + 0 + 2 + 0 = 42

Convert 10111 into decimal

Now let’s do the opposite. Since our binary number has 5 digits, it looks like this:

1 * 2⁴ + 0 * 2³ + 1 * 2² + 1 * 2¹ + 1 *2⁰

Now let’s calculate this:

16 + 0 + 4 + 2 + 1 = 23

Conclusion

I really hope this guide helped you to understand what binary numbers are or were a good refresher.