1. If you think base 2, 8, and 16 are weird compared to base 10, you should be glad that they are at least bitwise.

2. What is bitwise counting? That is, each bit has a clear meaning, and when it’s full, it carries. For example, the decimal 19, the first digit from right to left actually represents 9 10º, the second digit represents 1 10¹, if you add 1 to the first digit will be full of 20 which needs to be carried into decimal; Similarly, the binary 101 (equivalent to a decimal 5), from right to left the first digit represents a 2º, the second digit represents zero 2¹, the third digit represents a 2², and the first digit is filled with 110 (equivalent to a decimal 6) that needs to be carried into binary.

3. That being said, it would also mean that there were numeric representations that did not count in bits, known as Roman notation. 1) First understand the Symbols of Roman numeration, are I (1), V (5), X (10), L (50), C (100), D (500), M (1000); 2) Learn some special cases, such as 4 and 9 are not represented by IIII and VIIII, but by subtraction, i.e. IV and IX; 3) The last, most important and least important rule is that drawing a line over a number means multiplying it by 1000 times. This solves the problem of Roman numerals representing large numbers, but it’s really not a convenient way to write them.

4. With these three rules in mind, we can basically solve most Roman counting. For example, we represent the number 134,945,584, which is far more than 1000, so we must use multiples of 1000 to express it. We first break it down into: 134*1000*1000+945*1000+584, then we change to the Roman characters CXXXIV (134), CMXLV (945), DLXXXIV (584), and finally add a multiple of 1000 to make it:. If you look back at this number, from right to left, each bit doesn’t have a clear meaning, and you compute the value based on what symbol the current bit is occupied by or the symbols that precede it, which is pretty straightforward, so Roman counting isn’t bitwise counting.

5. Roman numerals are rarely seen these days, except when you buy a watch and Apple releases the iPhone X. The familiar and unfamiliar feeling of Roman numerals can be used as a setting in some retro or decryption games.

6. There are many short stories about Roman enumeration. If you are interested, refer to the encyclopaedia. The number 0, for example, was surreptitiously added in Roman numeracy against the Pope. So 0 is denoted by N, why N? Just as C (100) and M (1000) are the initials of Centum and Mille, N (0) is Nulla. Nulla means “empty.” It looks familiar.


From reading “Programmer’s Mathematics” by Jie Chenghao