Voyager golden record binary arithmetic

Question

I just read the article about the Voyager gold record cover,however, I do not understand the binary arithmetic of the left-hand corner, As you can see from the image below,, can some one please explain this binary arithmetic for me comprehensively? Thank you in advance.

Answer 1

The number for the "time of one rotation of the record" is read counterclockwise in the direction of the arrow. It reads as binary 100110000110010000000000000000000 which is decimal 5113380864.

The multiplier referred to as 0.7 ns is "the time period associated with a fundamental transition of the hydrogen atom". The hyperfine transition corresponds to the hydrogen line wavelength of 21.106 cm, or a period of 0.21106 / 299792458 = 0.704020379 ns.

Multiplying the two gives 5113380864 * 0.704020379 * 10^(-9) = 3.59992... seconds for one rotation, or approximately 3.6 seconds.

The other binary numbers translate in a similar way, for example the playing time is binary 1000010110000000000000000000000000000000000 = decimal 4587025072128. Converting to seconds gives 4587025072128 * 0.704020379 * 10^(-9) = 3229.3591... seconds, or approximately 58 minutes 49 seconds.