Binary
For DNA to be used as a storage system, the information must be coded. A simple way of accomplishing this is to use binary, a system common in today's computers. Binary is a base 2 system, with only two values used as digits, instead of the base 10 decimal system. The place within a number determines the value. Each place represents the base raised to a power. Because any base raised to the zeroth power is always one, there is always a ones place. In the decimal system, there is a tens place, a hundreds place, and so on. Binary uses powers of 2, so there is a twos place, a fours place, an eights place, and so on.
In base 10:
177 1 7 7 Hundreds Tens Ones 10^2 10^1 10^0 100+7(10)+7(1) = 100+70+7 = 177 There is a single 100, seven 10s, and seven 1s added together. |
In base 2:
10110001 1 0 1 1 0 0 0 1 128s 64s 32s 16s 8s 4s 2s 1s 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0 1(128)+0(64)+1(32)+1(16)+0(8)+0(4)+0(2)+1(1) = 128+32+16+1 = 177 There is a single 128, no 64s, a single 32, a single 16, no 8s, no 4s, no 2s, and a single 1 added together. |
Binary has been used by many tribes but the actual conscious development began in the mid-1600s with Gottfried Leibniz. Leibniz was dealing with logic, reducing things to simple statements. This was similar to a book he found that described life in opposites. Opposites such as yes-no, on-off, light-dark could be used, or most commonly, ones and zeros. This was applied to both real information and decisions, leading to the growth of Boolean logic, and can be applied to mathematics in general.