# The Binary Language of Computers

The binary math terms that follow are fundamental to understanding PC technology.

## Bits

A bit is the smallest unit of information that is recognized by a computer: a single on/off event.

## Bytes

A byte is a group of eight bits. A byte is required in order to represent one character of information. Pressing one key on a keyboard is equivalent to sending one byte of information to the CPU (the computer's central processing unit). A byte is the standard unit by which memory is measured in a computer-values are expressed in terms of kilobytes (KB) or megabytes (MB). The table that follows lists units of computer memory and their values.

Memory Unit Value
Bit Smallest unit of information, shorthand term for binary digit
Nibble 4 bits (Half of a byte)
Byte 8 bits (Equal to one character)
Word 16 bits on most personal computers (longer words possible on larger computers)
Kilobyte (KB) 1024 bytes
Megabyte (MB) 1,048,576 bytes (Approximately one million bytes or 1024 KB)
Gigabyte (GB) 1,073,741,824 bytes (Approximately one billion bytes or 1024 MB)

## The Binary System

The binary system of numbers uses the base of 2 (0 and 1). As described earlier, a bit can exist in only two states, on or off. When bits are represented visually:

• 0 (zero) equals off.
• 1 (one) equals on.

The following is one byte of information in which all eight bits are set to zero. In the binary system, this sequence of eight zeros represents a single character-the number 0.

``` 0     0     0     0     0     0     0     0
```

The binary system is one of several numerical systems that can be used for counting. It is similar to the decimal system, which we use to calculate everyday numbers and values. The prefix "dec" in the term "decimal system" comes from the Latin word for ten and denotes a base of ten. That is, the decimal system is based on the ten numbers zero through nine. The binary system has a base of two, the numbers zero and one.

## Counting in Binary Notation

Every schoolchild learns to count using the decimal system. There, the rightmost whole number (the number to the left of the decimal point) is the "digits" column. Numbers written there have a value of zero to nine. The number to the left of the digits column (if present) is valued from ten to ninety-the "tens" column. Ten is the factor of each additional row in the decimal system of notation. To get the total value of a number, we add together all columns in both systems: 111 is the sum of 100+10+1.

NOTE
A factor is an item that is multiplied in a multiplication problem. For example, 2 and 3 are factors in the problem 2 � 3.

In our more common decimal notation, the values of numbers are founded on a base of ten, starting with the rightmost column. Any number in that position can have a value ranging from zero to nine. In the next column to the left, the values range from 10 to 99; and in the column to the left of that, values range from 100 to 999. Binary notation uses a system of right-to-left columns of ascending values, but in which each row has only two-instead of 10-possible numbers.

Under the binary system, the first row to the right can be only zero or one; the next row to the left can be two or three (if a number exists in that position). The columns that follow have values of four, then eight, then sixteen, and so on, each column doubling the possible value of the one to its right. Two is the factor used in the binary system, and-just like decimal-zero is a number counted in that tally. Examples of bytes of information (eight rows) follow.

### Byte-Example A

The value of this byte is zero because all bits are off (0 = off).

```  0     0     0     0     0     0     0     0     8     bits
128   64    32    16    8     4     2     1     #     values
```

### Byte-Example B

In this example, two of the bits are turned on (1 = on). The total value of this byte is determined by adding the values associated with the bit positions that are on. This byte represents the number 5 (4 + 1).

```  0     0     0     0     0     1     0     1     8     bits
128   64    32    16    8     4     2     1     #     values
```

### Byte-Example C

In this example, two different bits are turned on to represent the number 9 (8 + 1).

```  0     0     0     0     1     0     0     1     8     bits
128   64    32    16    8     4     2     1     #     values
```

Those who are mathematically inclined will quickly realize that 256 is the largest number that can be represented by a single byte.

Because computers use binary numbers and humans use decimal numbers, A+ technicians must be able to perform simple conversions. The following table shows decimal numbers and their binary equivalents (0 to 9). You will need to know this information. The best way to prepare is to learn how to add in binary numbers, rather than merely memorizing the values.

Decimal Number Binary Equivalent
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001

Numbers are fine for calculating, but today's computers must handle text, sound, streaming video, images, and animation as well. To handle all of that, standard codes are needed to translate between binary machine language and the type of data being represented and presented to the human user. The first common code-based language was developed to handle text characters.

## Parallel and Serial Devices

The telegraph and the individual wires in our PCs are serial devices. This means that only one element of code can be sent at a time. Like a tunnel, there is only room for one person to pass through at one time. All electronic communications are-at some level-serial, because a single wire can have only two states: on or off.

To speed things up, we can add more wires. This allows simultaneous transmission of signals. Or, to continue our analogy, it's like adding another set of tunnels next to the first one; we still have only one person per tunnel, but we can get more people through because they are traveling in parallel. That is the difference between parallel and serial data transmission. In PC technology, we often string eight wires in a parallel set, allowing eight bits to be sent at once. This means that a single "send" can represent up to 256 numbers 28 = 256. That is the same number of values found in the ASCII code system (discussed in the next paragraph). Figure 2.1 illustrates serial and parallel communication. Figure 2.1 Serial and parallel communication