How to Read and Write Binary Numbers

How to Read Binary

To read a binary number:

1. Write a 1 above the rightmost binary digit.
2. Write a 2 above the next digit to the left and a 4 above the next digit.
3. Keep doubling the number written above as you move one digit to the left.
4. Add the numbers that are above the binary digits that contain a 1.

Example of Reading a Binary Number of 1011

We will use these steps to read the binary number of 1011.

Step 1. Write a 1 above the rightmost binary digit

The image below shows a 1 written above the rightmost digit of the binary number.

Step 2. Write a 2 above the next digit to the left and a 4 above the next digit

We write a 2 next to the 1 that was written previously.

We write a 4 next to this 2 as we move left.

Step 3. Keep doubling the number written above as you move one digit to the left

We have already written 1, 2 and 4 above the digits.

We have doubled 1 to get 2, doubled 2 to get 4 and now we double 4 to get 8.

We write an 8 above the next digit to the left.

Step 4. Add the numbers that are above the binary digits that contain a 1

In the binary digit of 1011, there are three digits of 1.

Above these ones, we have written a 1, 2 and an 8.

We add 8 + 2 + 1 = 11 to see that the binary number of 1011 is the number 11 in decimal form.

We did not add the 4 because this was above the 0.

In binary, a 1 means that we use the digit written above the number and a 0 means that we do not use it.

Examples of Reading Binary Numbers

Read the binary number: 10001.

Write the powers of 2 from right to left above the digits of the binary number. This is 16, 8, 4, 2, 1.

Add the powers of two that have a binary digit of 1 below them.

Here we have a 1 below 16 and 1, so we add 16 and 1 to get an answer of 17.

10001 is the binary way of writing the number 17.

For example, read the binary number of 110011.

The powers of two are written above the digits from right to left, starting with 1 on the right.

32, 16, 8, 4, 2, 1.

Add the powers of 2 that have a binary digit of 1 below them. That is 32, 16, 2 and 1.

1 + 2 + 16 + 32 = 51 and so, 110011 is the binary number that represents 51.

Binary numbers always start with a leading digit on the left hand side of 1. Binary numbers never start with a 0.

Even binary numbers always end in a 0. If a binary number ends in a 0, it is even.

Odd binary numbers always end in a 1. If a binary number ends in a 1, it is odd. This is because the digits of binary numbers represent powers of 2. The only odd power of 2 is the final binary digit of 1.

Here are some examples of converting binary to decimal numbers.

Binary Number	128	64	32	16	8	4	2	1	Sum	Decimal Number
101						1	0	1	4 + 1 =	5
111						1	1	1	4 + 2 + 1 =	7
1010					1	0	1	0	8 + 2 =	10
10100				1	0	1	0	0	16 + 4 =	20
101011			1	0	1	0	1	1	32 + 8 + 2 + 1 =	43
1010101		1	0	1	0	1	0	1	64 + 16 + 4 + 1 =	85
10110100	1	0	1	1	0	1	0	0	128 + 32 + 16 + 4 =	180

How to Write a Number in Binary

To write a number in binary, first write powers of 2 from right to left. For example: 16, 8, 4, 2, 1. Then place a 1 below the powers of 2 that add to make the number. Place a 0 below any powers of 2 that are not used. For example, 19 in binary is 10011 because the 5 digits of 10011 represent 16, 8, 4, 2 and 1 and the 16, 2 and 1 add to make 19.

For example, convert the decimal number of 50 into binary.

The powers of 2 are written above the binary number. We start with a 1 on the right and double as we go left.

We have 32, 16, 8, 4, 2, 1.

Now we select the powers of 2 from this list that add to make 50. That is 32 + 16 + 2.

We write a 1 below the 32, 16 and 2 columns and a 0 below the numbers that we did not use. We did not use an 8, 4 or 1, so we put a 0 in these columns.

50 in binary is 110010.

To convert a larger number to binary:

1. Subtract the largest power of 2 possible from the number
2. Write a 1 in the place value column below this power of 2
3. Subtract the largest power of 2 possible from the remainder
4. Write a 1 in the place value column below this power of 2
5. Continue doing this until there is a remainder of 0
6. Write a 0 in the place value columns below the powers of 2 not used

For example, convert 150 to binary.

We did not subtract 64, 32 or 8 in this process and so, we write a 0 in these place value columns.

150 in binary is 1001011.

List of Binary Numbers

The first ten binary numbers are 1, 10, 11, 100, 101, 110, 111, 1000, 1001 and 1010.

Here is a list of binary numbers from 1 to 100.

Number	Binary Number
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

How to Write a Decimal Number in Binary

In binary, the value of the digits to the left of the decimal point double as you go left. The value of the digits to the right of the decimal point halve as you go right. For example in the binary number 101.1, the place value columns represent 4, 2, 1 and then 0.5. Therefore 101.1 = 4 + 1 + 0.5, which is equal to 5.5.

Here is a binary number with a decimal point: 0.11.