The Arecibo Message
The message sent in 1974 from the Arecibo radio telescope toward the globular cluster M13 consisted of 1679 “bits” of information. A “0” is represented by an “off” radio pulse, while a “1” is represented by an “on” radio pulse.
0000001010101000000000000101000001010000000100100010001000100
1011001010101010101010100100100000000000000000000000000000000
0000011000000000000000000011010000000000000000000110100000000
0000000000101010000000000000000001111100000000000000000000000
0000000001100001110001100001100010000000000000110010000110100
0110001100001101011111011111011111011111000000000000000000000
0000010000000000000000010000000000000000000000000000100000000
0000000001111110000000000000111110000000000000000000000011000
0110000111000110001000000010000000001000011010000110001110011
0101111101111101111101111100000000000000000000000000100000011
0000000001000000000001100000000000000010000011000000000011111
1000001100000011111000000000011000000000000010000000010000000
0100000100000011000000010000000110000110000001000000000011000
1000011000000000000000110011000000000000011000100001100000000
0110000110000001000000010000001000000001000001000000011000000
0010001000000001100000000100010000000001000000010000010000000
1000000010000000100000000000011000000000110000000011000000000
1000111010110000000000010000000100000000000000100000111110000
0000000010000101110100101101100000010011100100111111101110000
1110000011011100000000010100000111011001000000101000001111110
0100000010100000110000001000001101100000000000000000000000000
0000000001110000010000000000000011101010001010101010100111000
0000001010101000000000000000010100000000000000111110000000000
0000001111111110000000000001110000000111000000000110000000000
0110000000110100000000010110000011001100000001100110000100010
1000001010001000010001001000100100010000000010001010001000000
0000001000010000100000000000010000000001000000000000001001010
00000000001111001111101001111000
This
picture was generated by arranging the 1679 bits above into 23
columns of 73 rows, 23 and 73 being the two prime numbers, which when
multiplied together equal 1679. A box representing a “one”
has been colored black, while a box representing “zero”
has been colored white. Unfortunately, the image is “parity
reversed, ” i.e., it was generated by scanning right to left,
i.e., the first bit in the message occupies the upper row, rightmost
cell. The next bit is the in the top row, next cell proceeding
to the left. Many books have printed the picture this way.
Maybe they think aliens are likely to be lefthanded or maybe it is
meant to tell them that all the amino acids that make up proteins in
life on Earth are “lefthanded” except for those that
have no handedness. You should be able to see, though, that the
"handedness" of the image is completely irrelevant
How to Count in Binary…
10 
1 
16 
8 
4 
2 
1 
Number 

10^{1} 
10^{0} 
2^{4} 
2^{3} 
2^{2} 
2^{1} 
2^{0} 

0 
0 
0 
0 
0 
0 
0 
0 

0 
1 
0 
0 
0 
0 
1 
1 

0 
2 
0 
0 
0 
1 
0 
2 

0 
3 
0 
0 
0 
1 
1 
3 

0 
4 
0 
0 
1 
0 
0 
4 

0 
5 
0 
0 
1 
0 
1 
5 

0 
6 
0 
0 
1 
1 
0 
6 

0 
7 
0 
0 
1 
1 
1 
7 

0 
8 
0 
1 
0 
0 
0 
8 

0 
9 
0 
1 
0 
0 
1 
8 

1 
0 
0 
1 
0 
1 
0 
10 

1 
1 
0 
1 
0 
1 
1 
11 

1 
2 
0 
1 
1 
0 
0 
12 

1 
3 
0 
1 
1 
0 
1 
13 

1 
4 
0 
1 
1 
1 
0 
14 

1 
5 
0 
1 
1 
1 
1 
15 

1 
6 
1 
0 
0 
0 
0 
16 

1 
7 
1 
0 
0 
0 
1 
17 

1 
8 
1 
0 
0 
1 
0 
18 

1 
9 
1 
0 
0 
1 
1 
19 

2 
0 
1 
0 
1 
0 
0 
20 
Our numbering system is “place based.” Each digit in a number represents that number times a base number raised to a power. For example, in the base 10 system, which we normally use to count, etc., the first place represents 10 raised to the power 0, which is 1. The second place (normally one place to the left of the first) represents 10 raised to the power 1, which is 10. The third place (the next place to the left) represents 10 raised to the power 2, which is 100, and so on. Each succeeding place is a power of ten higher than the preceding one. Thus, the base 10 number 378 means 3x100 + 7x10 + 8x1. Note 10 different digits, 0  9, are needed to represent all possible numbers in the base 10 system. The binary system works the same way … only the base number is 2  not 10! Thus, only two binary digits, called bits, are needed to represent all possible numbers. The possible bits are 0 and 1 (yes, any number can be represented by a “string” of 0’s and 1’s). Note that each succeeding place in the binary system is a power of 2 higher than the preceding one. You can see this pattern in the columns above where I have counted from 0 to 20 in both the base ten and binary systems. The Arecibo Message Explained
Here, I’ve redrawn the first figure according to normal convention by filling the cells left to right. In other words, the first bit occupies the leftmost, upper row cell, and so on. Also, I’ve colored the 1’s and left the 0’s black. The 1’s and 0’s form 7 ‘groupings’, essentially ‘sets of rows’ that represent some sort of information. For example, the first group reading from left to right, represents the numbers 110 in binary. The remaining groups are explained below the figure.
Group
1. Numbers 110
Group 2. Atomic numbers for H, C, N, O, P
Group 3. Formulas for sugars, bases and phosphate in DNA nucleotides
Group 4. Double helix structure of DNA surrounding binary number that represents the number of nucleotides in the human genome
Group 5. Height of human being marked on the left and human population marked on rightSchematic of solar system (human stands on 3^{rd} planet)
Group 6. Arecibo transmitting telescope
Group 7. Diameter of telescope
The first group bit pattern tells the aliens how humans count in binary from 110.
The pixels colored pink represent starting points, or beginning markers, for each binary number. The pixels marked in red are the binary digits (bits) 1. Pixels left black are bits 0. The first number on the left is 1. The next one is 2 (0 1 in binary). Notice, the least significant bit is at the bottom of a column (just above its respective “pink” marker  each succeeding bit is placed on top of the preceding one). There are 10 such groupings representing the numbers 1  10. Examining the encoded numbers 8, 9, and 10 reveals that when more significant bits are required than fit in a given dimension in the image, they continue in another row or column, starting next to the least significant bit of the previous row or column.
Directly below the numbers, which provide the key for interpreting its meaning, is the 2^{nd} group containing a list of four numbers which give the atomic numbers of the five chemical elements of which DNA is composed, and are the principal elements in all of the molecules of living things. From left to right (the same order as we found in the numbers above) we have:
Atomic 
Element 
1 
Hydrogen 
6 
Carbon 
7 
Nitrogen 
8 
Oxygen 
15 
Phosphorus 
I have colored the “1” bits representing these elements differently to provide a key to the section immediately below in the message. Hydrogen is colored grey, Carbonwhite, Nitrogenblue, Oxygenred, Phosphorusmagenta.
Group 
Formula 
Image 
Deoxyribose 
C_{5}OH_{7} 

Phosphate 
PO_{4} 

Adenine 
C_{5}H_{4}N_{5} 

Thymine 
C_{5}H_{5}N_{2}O_{2} 

Cytosine 
C_{4}H_{4}N_{3}O 

Guanine 
C_{5}H_{4}N_{5}O 

The chemical formulae for the molecular components of DNA are given in the table to the left. To aid in interpreting each encoded formula, the column giving the number of atoms for each element is colored the same as the corresponding column in the list of elements above. After figuring out the molecules from the encoded formula (which may be difficult, as only the number of atoms of each element is given with no indication of the structure), we can learn more about the overall structure of DNA from where the groups appear in image. First of all, we observe that the deoxyribosephosphate sequence is repeated twice on both the left and right sides of the image. To one acquainted with polymers, this suggests the chain may be of arbitrary length, with the basic unit repeating over and over. The appearance of the identical backbone sequence at both the left and right suggests a ladderlike structure.
The complementary base pairs are shown attached to the deoxyribose groups of the backbone, and the fact that Adenine pairs with Thymine and Cytosine with Guanine is indicated by the examples shown. If the recipient of the message managed to figure out the structural formula for each of the groups, further investigation of their chemistry would reveal that these were the only pairings possible, and thus suggest DNA is a molecule capable storing a large amount of data in coded form (the genetic code) making heredity and evolution possible.
Whether all of this could be figured out by a form of life completely unlike terrestrial biology (for example, sentient, selfreproducing computers made of silicon microchips, originally designed by a longextinct carbonbased life form, of which all memory has been lost) is an open question. We would hypothesize that they could.
Below the formulae for DNA is a schematic meant to indicate that its structure is a double helix. Assuming the aliens know some chemistry, this schematic would confirm the interpretation of the molecular components which they’ve just deduced. Knowing the molecule forms a helical structure would provide constraints useful in reducing ambiguity in the structure of the components of DNA. For example, if they synthesized the molecule using these components, they would see that DNA did indeed form a double helix, which would provide strong confirmation that its structure had been correctly decoded.
In the middle of the helix is a 32bit number, oriented along the axis of the helix to suggest it gives the length of the overall molecule. The number, about six billion, gives the approximate number of nucleotides in the human genome.
Directly below and slightly overlapping the helix, suggesting a relationship between them, is a cartoon depicting a human being. To an extraterrestrial that resembled a human being, this would immediately be read as "They look like us". Certainly, to a human, this is one of the most striking components of the message. What some alien critter would make of it is less obvious.
To the left of the figure representing the human are the binary digits 0111, representing the number 14 (remember, the least significant bit, the 0, starts next to the pink place marker). The number is written in the middle of a “bar” the same height as the human and meant to denote the height of the human. So the human is 14 tall. 14 what? The alien must figure out what unit of length the value 14 refers to. The only possible choice of scale is based on the universality of the speed of light c. In our units, it is c=3x10^{8} meters per second. Since the signal was broadcast at the frequency f = 2380 Mhz, the recipient knows the wavelength of the received message; L = c / f = 12.6 centimeters in our units ( some other number of “alien” units). This provides a length scale of measurement for the alien. Fourteen of these units is 176 cm, which is just about Frank Drake's own height.
At the right of the figure is another 32bit number, this one about four billion, intended to give the approximate human population (back in 1974  it’s 6+ billion now). Aliens who correctly interpret this will know how large an army to send.
Below the information about human beings is a schematic representating the Sun and planets of the solar system, which I've colored to make clearer which is which. The gas giants are all larger than the terrestrial planets, with Jupiter and Saturn indicated as larger than Uranus and Neptune to their right. Earth appears directly below the figure of the human and is offset in that direction, identifying it as the planet where humans live  third rock from the Sun.
The final item is a representation of the Arecibo antenna used to transmit the message, with dimension bars (as used with the human figure) and a number at the very bottom giving its approximate: binary 100101111110 (here reading the normal way since the pink place marker is the lower right pixel of the number between the dimension bars) or decimal 2430 units of the 12.6 centimeter wavelength of the message. This gives the size of the antenna as 30,618 centimeters, or about 306 meters.
The Search for Life in the Universe, Goldsmith and Owen, 3^{rd} ed., University Science Books