| Binary Numbers for Use on a PC or over the Internet |
Review binary numbers when considering the use of networks.
Reviewing Binary Numbers
In PCs or networks, digital signals, which represent “ON” or “OFF,” in other words, a signal whose value can only be “1” or “0,” are distributed.
By the way, do you remember something about the fact that a value is either “1” or “0”? That’s right, this is the “binary number” system. Thus, to learn about PCs or networks, you need a certain level of knowledge about binary numbers.
Before learning the fundamentals of the Internet, let’s have a quick review of binary numbers (You may have become familiar with this since you are taking assurance tests including questions on this every week).The table below shows the relationship between decimal numbers and binary numbers. See how they are related to each other.
| Decimal number | Divide by 2n | Binary number |
|---|---|---|
| 1k = 210, 1M = 220, 1G = 230 | ||
| Mutual conversion of a binary number and a decimal number | ||
Using the button at the bottom of the table above, convert the decimal numbers 10, 20, 40, and 80 into binary numbers respectively and confirm their relationship. In addition to this, convert the binary numbers 10000, 1000, 100, and 10 into their respective decimal numbers and confirm their relationship.
Here, just memorize the three points below.
- The binary number 1010 is the decimal number 10.
- 24 (the binary number 10000 (with 4 zeros) is the decimal number 16
- 28 (the binary number 100000000 (8 of 0) is a decimal number of 256
- 210 (1024) is 1k (kilo)
- 220 (10242) is 1M (mega)
- 230 (10243) is 1G (giga)
Amounts of Information (Bits and Bytes)
Binary numbers of one digit are “0” or “1”. This “0” or “1” can also be considered as a symbol that distinguishes two different states, such as “’obverse’ or ‘reverse’ (of a coin)” or “’ON’ or ‘OFF’ (of a switch).”
Then, how can we represent the four different states (seasons) of “spring,” “summer,” “fall,” and “winter” in binary numbers? We can represent them by using binary numbers of 2 digits as shown below.
| State (season) | spring | summer | fall | winter |
|---|---|---|---|---|
| Binary number | 00 | 01 | 10 | 11 |
As shown above, we can increase the number of states to be distinguished by increasing the digits of the binary number.
As a matter of fact, “distinguishing different states” has a close relationship to the “(amount of) information”.
“Information exists (having information)” can be considered as “making it possible to identify what is its state (phenomenon) among various different states (phenomenon).”
This might not be a very good example, however, think about the information on a lecturer in a university. Whether the lecturer is male or female, whether the lecturer’s age is over 45 years old or not, and whether the lecturer wears glasses or not are all “information” on the lecturer. The “information” “select (distinguish) specific properties that specify (identify) an individual among a group of people with various types of properties.” Each factor used to define it is what we call “information.”
Like “things that are black or white,” “specifying the one (state) from the two (states)” is the base unit (minimum unit) of “information.” Thus, information is based on a combination of “deciding between one or another” regarding various phenomenon. This minimum unit of “information” is called a bit in general. In the example of the lecturer above, it is the combination of the four factors of gender, age (whether over 45 years old or not), whether wearing glasses or not, and whether appointed as a lecturer to Basic Information Processing or not, therefore, this is “4-bit information.”
(Note) Bit is the abbreviation for binary digit.As described at the beginning of this section, one digit of a binary number can represent “two states distinctly,” so a bit is considered to correspond to a binary number. For example, 2 bits correspond to a binary number of two digits. Remember that the four seasons can be represented by 2 bits.
In addition, text data is often represented in 8 bits in a PC or on the Internet, therefore 8 bits is called 1 byte.
“Number” can be seen as representing the status of the “state of the number”.
For example, imagine an uncivilized country where people only use “none,” “one,” “two,” and “plenty” to count things (in reality, there is no country like this). Thus, in this country, things that are more than “two” are counted as “plenty,” even if there are 3 of them, or 1,000 of them, everything is counted as “plenty” with no distinction.
That’s right, the reason is that they distinguish only 4 states when they count things. It can be represented using numbers with one digit such as 0, 1, 2, and 3, and 3 represents all numbers (states) more than 2.
If you represent it using only the numeric characters 0 and 1, thus using binary numbers, every number can be represented in two digits. In this case, “11” represents all numbers (states) except “00,” “01,” and “10.”
As opposed to the country described above, we distinguish all numbers, so this would never be enough no matter how many numbers we create. Therefore, we increase the number of digits as necessary to represent (distinguish) numbers (states).