The vast majority of us are familiar with decimals and the base-10 number system. We use the base-10 number system in our everyday counting.
Fewer people are familiar with the binary system. Binary is a number system that plays an important role in storing information for computers.
In this article, we’ll talk about what decimals are, what binaries are, and how to convert between the two.
What Are Decimals?
The decimal or base-10 numbering system is the number system we encounter most often.
In the decimal numbering system, there are 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Each integer number column in the decimal numbering system has a value of units. Each position to the left of the decimal point has an increased positive power of 10. Each position to the right of the decimal point becomes more negative by the power of ten.
Let’s take the number 549.
The farthest right number, 9, is in the 1s column. It is closest to the decimal point. The number 9 indicates that there are nine ones. The next number from right, 4, is in the 10s column. The number 4 there indicates that the number is actually 40. The final number, 5, is in the hundreds place. That indicates that there are 5 hundreds (500).
What Are Binaries?
The binary system, on the other hand, is a base-2 system. While the decimal system has values from 0 to 9, the base-2 (or binary) system only has values of 0 or 1.
In this binary number system, each digit from right to left has a value twice that of the previous digit. So, the value of binary positions, starting on the right, are:
1, 2, 4, 8, 16, 32, 64, and so on.
Let’s look at the binary number 11.
There is 1 in the 1s column and 1 in the 2s column. So 1 + 2 = 3.
The number 11 = 3.
Let’s try another number: 1101.
There is 1 in the 1s column, 0 in the 2s column, 1 in the 4s column, and 1 in the 8s column.
So, we have 1 + 4 + 8 = 13.
The number 1101 = 13.
Binary to Decimal Converter: Equivalents
Here’s a handy chart that shows you numbers 0 - 9 converted to binary
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Decimal
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Binary
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0
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0
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1
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1
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2
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10
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3
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11
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4
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100
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5
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101
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6
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110
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7
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111
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8
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1000
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9
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1001
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How to Convert Binary to Decimal
You can easily convert from binary to decimal using a strategy called the remainder method. Let’s look at those steps.
#1: Write Down the Decimal Number
We’ll start with 29.
#2: Divide the Number by 2 and Take Note of the Remainder
29 / 2 = 14, remainder 1
#3: Divide the Whole Number Result by 2 and Take Note of the Remainder
14 / 2 = 7, remainder 0
#4: Repeat Step 3 Until the Result of the Division Is 0
7 / 2 = 3, remainder 1
3 / 2 = 1, remainder 1
1 / 2 = 0, remainder 1
0
#5: Read the Remainders Back From Bottom to Top
29 = 11101
How to Convert Binary to Decimal
In order to convert from binary to decimal, you need to multiply the value of the digit by the placeholder in the number.
Let’s try it.
#1: Write Down the Number
101110
#2: Multiply Each Digit by Its Placeholder
Remember, in binary number system, each digit from right to left has a value twice that of the previous digit. So, the value of binary positions, starting on the right, are:
1, 2, 4, 8, 16, 32, 64, and so on.
0 X 1 = 0
1 X 2 = 2
1 X 4 = 4
1 X 8 = 8
0 X 16 = 0
1 X 32 = 32
#3: Add up all the Results
Take the values you’ve determined and add them all together
2 + 4 + 8 + 32 = 46
#4: The Result Is Your Decimal Number
101110 binary = 46 decimal
How to Convert Binary to Decimal: Key Tips
Converting binary to decimal (or the other way around) can be tricky. Here are some tips to remember how to do each.
#1: Remember the Values for Each Binary Place
One of the biggest places you can get tripped up on your binary to decimal converter is if you use the wrong place value for the binary places. Remember, each binary place is worth twice the place value before it. If you find yourself making a mistake or forgetting which value is which, you might need to...
#2: Make a Table
Our second tip is to make a table. If you’re forgetting values, staying organized by making a table can help you. Write the value of the binary place, then leave a row for you to input the 1 or 0 place value. That way you can easily see what value is what.
Decimal to Binary Converter: Sample Problems
Here are some decimal to binary sample problems. Try to write them and see if you get the correct answer.
#1: Write 16 in Base 2
Solution: 10000
#2: Write 33 in Base 2
Solution: 110001
#3: Write 19 in Base 2
Solution: 10011
Binary to Decimal Converter: Final Thoughts
Binaries and decimals are two different number systems. You can convert between the two systems easily using the systems outlined in this article.
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