Discuss with your partner the following question.

· How bits and bytes relate to the size of digital storage devices?

4. Skim the text to check your ideas.

HOW BITS & BYTES WORK

If you have used a computer for more than five minutes, then you have heard the words bits and bytes. Both RAM and hard disk capacities are measured in bytes, as are file sizes when you examine them in a file viewer. You might hear an advertisement that says, "This computer has a 32-bit Pentium processor with 64 megabytes of RAM and 2.1 gigabytes of hard disk space." In this article, we will discuss bits and bytes so that you have a complete understanding.

The easiest way to understand bits is to compare them to something you know: digits. A digit is a single place that can hold numerical values between 0 and 9. Digits are normally combined together in groups to create larger numbers. For example, 6,357 has four digits. It is understood that in the number 6,357, the 7 is filling the "1s place," while the 5 is filling the 10s place, the 3 is filling the 100s place and the 6 is filling the 1,000s place. So you could express things this way if you wanted to be explicit:

(6 * 1000) + (3 * 100) + (5 * 10) + (7 * 1) = 6000 + 300 + 50 + 7 = 6357

Another way to express it would be to use powers of 10. Assuming  that we are going to represent the concept of "raised to the power of" with the "^" symbol (so "10 squared" is written as "10^2"), another way to express it is like this:

(6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357

What you can see from this expression is that each digit is a placeholder for the next higher power of 10, starting in the first digit with 10 raised to the power of zero.

That should all feel pretty comfortable -- we work with decimal digits every day. The neat thing about number systems is that there is nothing that forces you to have 10 different values in a digit. Our base-10 number system likely grew up because we have 10 fingers, but if we happened to evolve to have eight fingers instead, we would probably have a base-8 number system. Computers happen to operate using the base-2 number system, also known as the binary number system (just like the base-10 number system is known as the decimal number system).

The reason computers use the base-2 system is because it makes it a lot easier to implement them with current electronic technology. You could wire up and build computers that operate in base-10, but they would be fiendishly expensive right now. On the other hand, base-2 computers are relatively cheap.

So computers use binary numbers, and therefore use binary digits in place of decimal digits. The word bit is a shortening of the words "Binary digIT." Whereas decimal digits have 10 possible values ranging from 0 to 9, bits have only two possible values: 0 and 1. Therefore, a binary number is composed of only 0s and 1s, like this: 1011. How do you figure out what the value of the binary number 1011 is? You do it in the same way we did it above for 6357, but you use a base of 2 instead of a base of 10. So:

(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11

You can see that in binary numbers, each bit holds the value of increasing powers of 2. That makes counting in binary pretty easy. Starting at zero and going through 20, counting in decimal and binary looks like this:

0 = 0  1 = 1  2 = 10  3 = 11  4 = 100  5 = 101  6 = 110  7 = 111  8 = 1000  9 = 1001 10 = 1010 11 = 1011 12 = 1100 13 = 1101 14 = 1110 15 = 1111 16 = 10000 17 = 10001 18 = 10010 19 = 10011 20 = 10100

When you look at this sequence, 0 and 1 are the same for decimal and binary number systems. At the number 2, you see carrying first take place in the binary system. If a bit is 1, and you add 1 to it, the bit becomes 0 and the next bit becomes 1. In the transition from 15 to 16 this effect rolls over through 4 bits, turning 1111 into 10000. Bits are rarely seen alone in computers. They are almost always bundled together into 8-bit collections, and these collections are called bytes. Why are there 8 bits in a byte? A similar question is, "Why are there 12 eggs in a dozen?" The 8-bit byte is something that people settled on through trial and error over the past 50 years. With 8 bits in a byte, you can represent 256 values ranging from 0 to 255, as shown here: 0 = 00000000 1 = 00000001 2 = 00000010... 254 = 11111110 255 = 11111111

Next, we'll look at one way that bytes are used. Bytes are frequently used to hold individual characters in a text document. In the ASCII character set (see Appendix), each binary value between 0 and 127 is given a specific character. Most computers extend the ASCII character set to use the full range of 256 characters available in a byte. The upper 128 characters handle special things like accented characters from common foreign languages.

You can see in the Appendix the 127 standard ASCII codes below. Computers store text documents, both on disk and in memory, using these codes. For example, if you use Notepad in Windows 95/98 to create a text file containing the words, "Four score and seven years ago," Notepad would use 1 byte of memory per character (including 1 byte for each space character between the words -- ASCII character 32). When Notepad stores the sentence in a file on disk, the file will also contain 1 byte per character and per space.

Try this experiment: Open up a new file in Notepad and insert the sentence, "Four score and seven years ago" in it. Save the file to disk under the name getty.txt. Then use the explorer and look at the size of the file. You will find that the file has a size of 30 bytes on disk: 1 byte for each character. If you add another word to the end of the sentence and re-save it, the file size will jump to the appropriate number of bytes. Each character consumes a byte.

If you were to look at the file as a computer looks at it, you would find that each byte contains not a letter but a number -- the number is the ASCII code corresponding to the character (see below). So on disk, the numbers for the file look like this:

 F o u  r      a n d         s e v e n
70 111 117 114 32 97 110 100 32 115 101 118 101 110

By looking in the ASCII table, you can see a one-to-one correspondence between each character and the ASCII code used. Note the use of 32 for a space -- 32 is the ASCII code for a space. We could expand these decimal numbers out to binary numbers (so 32 = 00100000) if we wanted to be technically correct -- that is how the computer really deals with things.

The first 32 values (0 through 31) are codes for things like carriage return and line feed. The space character is the 33rd value, followed by punctuation, digits, uppercase characters (символыверхнегорегистра) and lowercase characters. To see all 127 values, check out Unicode.org's chart (http://www.unicode.org/charts/PDF/U0000.pdf).

When you start talking about lots of bytes, you get into prefixes like kilo, mega and giga, as in kilobyte, megabyte and gigabyte (also shortened to K, M and G, as in Kbytes, Mbytes and Gbytes or KB, MB and GB). The following table shows the binary multipliers:

Name	Abbr.	Size
Kilo	K	2^10 = 1,024
Mega	M	2^20 = 1,048,576
Giga	G	2^30 = 1,073,741,824
Tera	T	2^40 = 1,099,511,627,776
Peta	P	2^50 = 1,125,899,906,842,624
Exa	E	2^60 = 1,152,921,504,606,846,976
Zetta	Z	2^70 = 1,180,591,620,717,411,303,424
Yotta	Y	2^80 = 1,208,925,819,614,629,174,706,176

You can see in this chart that kilo is about a thousand, mega is about a million, giga is about a billion, and so on.

When you consider that one CD holds 650 megabytes, you can see that just three CDs worth of data will fill the whole thing! Terabyte databases are fairly common these days, and there are probably a few petabyte databases floating around the Pentagon by now.

Binary math works just like decimal math, except that the value of each bit can be only 0 or 1. To get a feel for binary math, let's start with decimal addition and see how it works. Assume that we want to add 452 and 751:

452
+ 751
---
 1203

To add these two numbers together, you start at the right: 2 + 1 = 3. No problem. Next, 5 + 5 = 10, so you save the zero and carry the 1 over to the next place. Next, 4 + 7 + 1 (because of the carry) = 12, so you save the 2 and carry the 1. Finally, 0 + 0 + 1 = 1. So the answer is 1203.

Binary addition works exactly the same way:

010
+ 111
---
 1001

Starting at the right, 0 + 1 = 1 for the first digit. No carrying there. You've got 1 + 1 = 10 for the second digit, so save the 0 and carry the 1. For the third digit, 0 + 1 + 1 = 10, so save the zero and carry the 1. For the last digit, 0 + 0 + 1 = 1. So the answer is 1001. If you translate everything over to decimal you can see it is correct: 2 + 7 = 9.

To sum up, here's what we've learned about bits and bytes:

· Bits are binary digits. A bit can hold the value 0 or 1.

· Bytes are made up of 8 bits each.

· Binary math works just like decimal math, but each bit can have a value of only 0 or 1.

5. Find and learn Russian equivalents for the following words and expressions:

 

1) numerical value	a)
2) decimal digit	b)
3) binary number system	c)
4) bundled together	d)
5) accented characters	e)
6) carriage return (CR)	f)
7) uppercase character	g)
8) prefix	h)
9)zettabyte	i)
10) petabyte	j)
11) hexadecimal	k)

6. Find and learn English equivalents for the following words and expressions:

1) указатель места заполнения, структурный нуль	a)
2) степень десятки	b)
3) в квадрате	c)
4) десятичная система счисления	d)
5) стандартный набор символов ASCII	e)
6) взаимнооднозначноесоответствие	f)
7) перевод строки	g)
8) нижний регистр	h)
9) двоичныйумножитель	i)
10) приставка, обозначающая квинтильон, или 2 в степени 60	j)
11) септибайт единица ёмкости памяти, равная 1024 секстибайт или 2 в степени 80	k)

 

ASCII characterset

Acronym for American Standard Codefor Information Interchange.128 characters that make up the ASCII coding scheme.

Binary

Consisting of only two integers, 0 and 1. Binary math is the basis for manipulating all data in computers.

binary number system

A method of representing numbers in which only the digits 0 and 1 are used. Successive units are powers of 2. Also called binary system.

carriage return

The operation that prepares for the next character to be printed or displayed as the first character on a line.

gigabyte

A unit of computer memory or data storage

capacity equal to 1,024 megabytes (2³⁰ bytes).

line feed

The operation that prepares for the next character to be printed or displayed on the next line.

megabyte

The prefix mega- often does not have its standard scientific meaning of 1,000,000, but refers instead to the power of two closest to 1,000,000, which is 2²⁰, or 1,048,576. The calculation of data storage capacity (measured in bytes) is based on powers of two because of the binary nature of bits (1 byte is 8, or 2³, bits). Thus, a megabyte is 1,048,576 bytes, although it is also used less technically to refer to a million bytes. Other numerical prefixes are interpreted similarly. With data transmission rates (measured in bits per second), a bit is considered as a signal pulse, and calculations are generally based on powers of ten. Thus, a rate of one megabit per second is equal to one million bits per second. However, in certain technical contexts, megabit can also refer to 1,048,576 bits.

placeholder

A symbol in a logical or mathematical expression that can be replaced by the name of any member of specified set.

! Study the following sentence: Assuming that we are going to represent the concept of " raised to the power of" with the "^" symbol …

Present Participles (verb +ing) describe what something or somebody is.

Past Participles (verb +ed/V3) describe how someone feels.

! Most past participles have passive meaning and can often be used as adjectives before nouns, or after be and other linking verbs, e.g. measured bytes = (bytes that have been measured, accented symbol = (symbol that have been accented)

! An – ing/ed forms with an object can be used as an adjective. Note the word order, e.g. contact-logging tool, a room-sized computer

! Used like adjectives or adverbs have similar meaning to active verbs, e.g. floating databases = (databases that float)

! We often use participles after nouns in order to define or identify the nouns, in the same way as we use identifying relative clauses, e.g. We couldn't agree on any of the trials presented. = (trials that were presented)

! A few past participles can be used as adjectives with active meaning, especially before nouns, e.g. advanced agrotechnics = (agrotechnics that have advanced to a high level, developed economy             

7. Find and underline other examples of participles in the text.

8. Underline the correct item.

1) The new program was exciting / excited.

2) What happens to your discarded / discarding old computer?

3) Bytes and bits are the starting / started point of the computer world.

4) Americans own billions of electronic products, including / included 200 million computers.

5) E-waste also includes cell phones, DVD players, video cameras and answering / answered machines.

6) Is what we're recycling / recycled actually getting recycled / recycling?

7) The "ray" is a stream of electrons generated / generating by an electron gun that naturally pour off a heated /heating cathode into the vacuum.

8) Random access memory is the most well-known form of computer memory, because it determines how quickly and efficiently your computer can perform your requested / requesting tasks.

9) There are several types of computer memory that are arranged based / basing on both technical and financial concerns.

10) There are several types of computer memory that are arranged based / basing on both technical and financial concerns.

9. Find the mistakes and correct the sentence.

1) By reversed the direction of the current, the drive magnetizes particles in the metallic coating on a disk so the particles' north and south poles are oriented to create combinations represented a 0 ar a 1 bit.

2) After subtracted the overhead for packet packaging, the basic PCI-Express slot has a top bandwidth of 250 megabytes a second.

3) A lowercase "g" and "q" can both contain closing loops whose distinctions are too subtle far a computer to recognize.

4) It also performs the same CRC operation that was performed on the packet before its journey and compares its result to the earlier one bundling into the packet.

5) What's really happening is actually digital -- representing by discrete, separate, and different numerical values.

10. Translate the following sentences into Russian.

1) After an image processor in the camera massages the visual data passed on by the sensor, the processor converts the image to a system of numerical values that represent different colors and hues.

2) Some OCR programs also display a magnified bitmap onscreen and ask you to press the key of the character needed to substitute for the placeholder character.

3) A capital "A" is 65. A capital "B" is 66. A lowercase"b" is98.

4) Their ability to move data is indicated by the multiplier factor in their designations.

5) In machine language, the hexadecimal code 40 increases by one the value contained in the register named AX.

 

11. Translate the following sentences into English.

1. Лейбниц описал современную двоичную систему счисления и в 1679 году он представил модель своей бинарной арифметики.

2. Коды представляют символы, знаки препинания и движения принтера такие как табуляции, возврат каретки,перевод строки и прогон страницы являющийся управляющим символом, используемым при печати на принтере для перехода к новой странице.

3. Верхний и нижний регистры имеют разныйнабор ASCII-символов.

4. CD диск вмещает 650 мегабайтов данных.

5. Формы и цвета, несомненно, являются такой же информацией, как и слова.

 

 

12. Answer the following questions.

1) What are bits and bytes?

2) Why do computers use the base-2 system?

3) How can binary code represent so many more numbers than just 0 and 1?

4) When someone says, "This computer has a 2 gig hard drive," what does he or she mean? (that the hard drive stores 2 gigabytes, or approximately 2 billion bytes, or exactly 2,147,483,648 bytes)

5) How could you possibly need 2 gigabytes of space?

6) When you start talking about lots of bytes, what prefixes do you get into?

13. Topics for discussion.

1. Working with bits and bytes.

2. Undesired Fonts used for ASCII Text.

 

14. Prepare a presentation on the topic being discussed.

 

1. Brain, Marshall. " How Bits and Bytes Work ",April2000./http://www.howstuffworks.com/

2. How computer works’, by Ron White, 2008, pp.8-9.

Appendix