The data would compress well, true. However, the DNA in the cell doesn’t have anything like data compression, and it makes the calculations more complex, so it’s only fair to compare uncompressed sizes.
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The full genome is 3.1 billion base pairs (6.2 Gbit = 775 MByte). Each parent (i.e., one egg or one sperm) contributes half of that, 1.55 billion base pairs (3.1 Gbit = 388 MByte).
Each base-pair requires two bits, not four. Picking an arbitrary convention: 00 = A, 01 = T, 10 = G, 11 = C.
This calculation is off by an order of magnitude.
The human genome has about 3.1 billion base pairs. Each sperm has half of that. Ignoring epigenetics, each base pair has four options (A/T/C/G), so it can be represented by two bits each.
All told, that’s 3.1 gigabits = 388 megabytes per gamete.
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According to this sign, he is the ssecretary of war.