Convert Decimal to Binary!

This Decimal to Binary Converter lets you convert any Decimal number to Binary quickly and easily.

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How to use the Decimal to Binary Converter

Converter features

🔢 Decimal Input length:	Up to 7 digits
⚡ Conversion Speed:	Instant!
➡️ Binary Output:	Display, Copy, Save
🎯 Conversion Accuracy:	100%

Read (or watch) our tutorial on How to Convert Decimal to Binary to learn more about the process of converting decimal numbers to binary.

Try the Binary to Decimal Converter too!

How to Convert Decimal to Binary

If you work with computers, you may find yourself needing a basic understanding of the binary number system.  Or, maybe you just want to know binary for fun. Either way, understanding how to convert from decimal number system to binary number system can be a useful tool.

Here’s the best part: you don’t need a degree in math or a decimal to binary calculator do it.

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Ones and Zeros

You can think of binary as the language computers speak.  It is made up by a series of ones and zeros.  At first glance, it may look like madness, but there is a method to it.  We’ll start with a simple, single-digit, and explain how you can convert a decimal to binary.  Let’s use the number 7.

Decimal to binary conversion involves redefining the number you wish to convert.  7 can be represented as simply 7. Or, it can be represented as 4+3.  Rewriting the number is the first step in converting to binary. Most importantly, we want to dissect our decimal into the sum of powers of 2.

So let’s look at 7, and let’s consider the powers of 2.  What power of 2 is closest to the number 7 while being equal or less than 7?

2² gives us 4, so we’re going to use 4 to start disassembling 7.  We must add 3 to make up the rest of 7.  So now, we can consider 7=4+3.

It might be helpful to have a table of powers of 2 for reference.  We’ve included part of the table in the picture below.

Now we have 3, but there are no powers of 2 that give us 3.  We must break down 3 in the same way we did 7.  So, find the sum of powers of 2 that will give us 3.  Remember, we must begin with powers of 2 equal or less than 3.  2¹ gives us 2, and 2⁰ gives us 1.

We used three different powers of 2 in this example.  So, the binary representation of 7 will be three digits long.  Since the highest power of 2 we needed was 2², we’re going to start by counting how many times 2² was used.  In binary, there can only be two answers to this question: it was used one, or zero times. If we did use it, we’ll indicate it with a 1.  If not, we’ll indicate it with a 0.

Using 2² means we’ll mark down a 1.  Now, we work down, counting the rest of powers of 2 we used.  We used 2¹, so we’ll indicate it with another 1. We used 2⁰, so we’ll use 1 in the final spot.

We now have the decimal 7 converted into binary, as 111.

We can use 8 as an even easier example of how to convert decimal to binary.  What power of 2 is equal or less than 8? 2³ gives us 8 exactly, so we don’t need to deconstruct anything.

We used 2³ once.  We used 2², 2¹, and 2⁰ zero times.  So 8 gives us 1000 in binary.  Binary is simply counting how many times you used a power of 2 to break down your decimal.

Does that mean if we want to write the decimal 78 in binary, we can combine the binary equivalents in each digit?  111 and 1000?  Well, not exactly. 1111000 translates to 120!  But if we want to translate 78 to binary, it’s as easy as translating a single decimal value.

Same as before, we’ll look at which power of 2 is closest to 78.  2⁶ gives us 64, which is the closest to 78 we can find without going over 78.  We can redefine 78 as 78 = 64 + 14.

Now we must redefine 14 as well.  We can use 2³ to give us 8, and now we need to add 6 to make 14.  Since 6 isn’t an exponent of 2 either, it needs to be deconstructed into a sum of powers of 2.

Lucky for us, 2² gives us 4, and 2¹ gives us 2.  Now, no more numbers need to be deconstructed, and we can turn it into binary.  Since we started all the way at 2⁶ we must ask if we used that power, and each one that came before it, back to 2⁰.

How many times did we use 2⁶? 1

How many times did we use 2⁵? 0

How many times did we use 2⁴? 0

How many times did we use 2³? 1

How many times did we use 2²? 1

How many times did we use 2¹? 1

How many times did we use 2⁰? 0

So, 78 in binary is 1001110

Not as scary as you thought, right?  The same algorithm works for three digit decimals and upwards.  The only difference is you might need a more extensive table of powers of 2 (or a calculator) in order to work through the equation.  Or, you can use a decimal to binary converter for larger numbers, like the one at the top of this page.  Bottom line; converting decimal to binary is as easy as 1, 2, 3 – or shall we say, 1, 10, 11!

Table of the First hundred Decimal numbers in Binary

For your convenience, the following table shows the decimal numbers from 0 to 100 along with their Binary representation.

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
11	1011
12	1100
13	1101
14	1110
15	1111
16	10000
17	10001
18	10010
19	10011
20	10100
21	10101
22	10110
23	10111
24	11000
25	11001
26	11010
27	11011
28	11100
29	11101
30	11110
31	11111
32	100000
33	100001
34	100010
35	100011
36	100100
37	100101
38	100110
39	100111
40	101000
41	101001
42	101010
43	101011
44	101100
45	101101
46	101110
47	101111
48	110000
49	110001
50	110010
51	110011
52	110100
53	110101
54	110110
55	110111
56	111000
57	111001
58	111010
59	111011
60	111100
61	111101
62	111110
63	111111
64	1000000
65	1000001
66	1000010
67	1000011
68	1000100
69	1000101
70	1000110
71	1000111
72	1001000
73	1001001
74	1001010
75	1001011
76	1001100
77	1001101
78	1001110
79	1001111
80	1010000
81	1010001
82	1010010
83	1010011
84	1010100
85	1010101
86	1010110
87	1010111
88	1011000
89	1011001
90	1011010
91	1011011
92	1011100
93	1011101
94	1011110
95	1011111
96	1100000
97	1100001
98	1100010
99	1100011
100	1100100

Questions and Answers about Decimal to Binary conversion