# BITS and BYTES

Because computers are made up of digital electronics, internally they respond to two kinds of electrical states: "on" or "off". These may actually be high or low voltage, positive and negative voltage, or some other combination. The key is that there are two conditions. We represent these with two numbers: 0 and 1, and the arithmetic that deals with these two states is called binary arithmetic. The only Digits in the Binary system are 0 and 1.

Each 0 or 1 in the binary system is termed a bit (short for Binary digit.

Strings of bits are used to represent numbers larger than 1 (much like combinations of digits are used to represent numbers larger than 9 in our decimal numbering system.

Bits in strings of eight are called bytes, and one byte usually represents a single character of data in the computer. It's a little used term, but you might be interested in knowing that a nibble is half a byte (usually 4 bits).

Bits and Bytes are used to measure download speeds from the Internet. What are kbps?

kbps or Kilo Bits Per Second is the rate at which 1000 bits of data travels across your internet connection. A bit is the smallest unit of digital information. 8 bits make up 1 byte. This is a screen shot showing a file being downloaded. Notice the transfer rate of 121 KB/Sec.

This is Kilo Bytes per second.

This number does not reflect your actual connection speed.  Connection Speeds are measured in Kilo Bits Per Second, not Kilo Bytes.

In this case my connection speed is 8 times the Transfer Rate or 968 kbps.

Binary Numbers Explained

Let's look at the concept of binary numbers and bytes a little closer.

Think of binary numbers in terms of switches. With two switches you can represent up to four different numbers.

0 0 (OFF OFF) = Decimal 0
0 1 (OFF ON) = Decimal 1
1 0 (ON OFF) = Decimal 2
1 1 (ON ON) = Decimal 3

Study the above for a moment -- it brings out an important concept in computers. Do you see it?

Look at the decimal number versus the number of numbers. Two binary numbers gives you up to decimal 3, but there are four actual numbers. In our decimal system, we rarely think of the zero; with computers, zero is always thought of as a number.

Thus, a single bit represents 2 numbers, two bits give 4 numbers, three bits show 8 numbers, four bits represent 16 numbers, and so forth up to a byte, or eight bits, which represents 256 numbers. (Each added bit doubles the number of numbers.) But, while 8 bits represents 256 numbers the byte 11111111 equals decimal 255.

Just to show you the correspondence between binary and decimal numbers here is a table that runs down a few:

Binary numbers are formed just like decimal, except there are only two numbers to work with. Exhaust those two numbers and start over with the next position to the left filled with a "1".

When you are down to 111 you simply start the entire marked series over again with a 1 in front of it. Thus, every time you add a binary digit to the string you effectively double the number of total decimal numbers available for use.

Look at the table. One bit counts to two numbers, two bits count to four numbers, three bits to eight numbers, four bits to 16 numbers, five to 32, six to 64, seven to 128 and finally, one byte (8 bits) counts to 256 numbers.

Decimal   Binary Representation
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

It is easy to get confused over the point of zero being a digit. A byte with all digits ON represents the decimal number 255 and it is hard to visualize this as the 256th digit in a series, but that is exactly what the computer demands of you.

In brief -- start learning to count from zero, not one!

# Kilobytes and Megabytes

The first place we will use the concept of counting in binary is in talking about computer memory. Early manufacturers stated memory capacity in terms of kilobytes. In the decimal system, the prefix kilo- means 1,000. In the binary system the prefix kilo- means 1,024.

It's a little tricky, but 1,024 is 2 to the 10th power, or the number that can be represented by 10 bits that are all set to one. Thus, ten ones in a row represents the decimal number 1,023 and the 1,024th digit. Using this nomenclature, a computer may be described as having 640K (640 kilobytes) of memory, when it really has 640 x 1,024 or 655,360 bytes.

By the same token, computers are described as having megabytes and gigabytes of memory, even though there is somewhat more than a million or billion actual bytes available. When 64-bit CPU's become common memory will start to be spoken about in terabytes, petabytes, and exabytes.

One kilobyte equals 2 to the 10th power, or 1,024 bytes.
One megabyte equals 2 to the 20th power, or 1,048,576 bytes.
One gigabyte equals 2 to the 30th power, or 1,073,741,824 bytes.
One terabyte equals 2 to the 40th power, or 1,099511,627,776 bytes.
One petabyte equals 2 to the 50th power, or 1,125,899,906,842,624 bytes.
One exabyte equals 2 to the 60th power, or 1,152,921,504,606,846,976 bytes.
One zettabyte equals 2 to the 70th power, or 1,180,591,620,717,411,303,424
One yottabyte equals 2 to the 80th power, or 1,208,925,819,614,629,174,706,176

Note: There is some lack of standardization on these terms when applied to memory and disk capacity. Memory specifications tend to adhere to the definitions above whereas disk capacity specifications tend to simplify things to the 10th power definitions (kilo=103, mega=106, giga=109, etc.) in order to produce even numbers.

Some other units of measurement you may come across:

Frequency Multipliers

HZ - Hertz - Cycles Per second
KHZ - Kilohertz - one thousand hertz
MHZ - Megahertz - one million hertz
GHZ - gigahertz - one billion hertz
THZ - Terahertz - one trillion hertz

Radio Frequency Bands

Extremely Low Frequency - ELF - Frequency 3 to 30 HZ - Wavelength: 100,000 to 10,000 KM
Super Low Frequency - SLF - 30-300 HZ; 10,000-1,000 KM
Ultra Low Frequency - ULF - 300-3000 HZ; 1,000-100 KM
Very Low Frequency - VLF - 3-30 KHZ; 100-10 KM
Low Frequency - LF - 30-300 KHZ; 10-1 KM
Medium Frequency - MF - 300-3000 KHZ; 1 KM - 100 M
High Frequency - HF - 3-30 MHZ; 100-10 M
Very High Frequency - VHF - 30-300 MHZ; 10-1 M
Ultra High Frequency - UHF - 300-3000 MHZ; 1M - 10CM
Super High Frequency - SHF - 3-30 GHZ; 10-1 CM
Extremely High Frequency - EHF - 30-300 GHZ; 1 CM - 1 MM

The wavelength of a radio frequency (sinusoidal wave) is the distance between consecutive corresponding points of the same phase; or  to make it simple.  Peak to Peak distance. The Wavelength of any frequency can be found by the formula: velocity divided by frequency. Velocity is fixed at the speed of light: 300,000 kilometres per second. That is why your VHF TV antenna is larger than your UHF TV antenna. The higher the frequency the shorter the wavelength. Antennas must be designed so that the elements of the antenna fit into the wavelength of the frequency being transmitted. Some antennas are quarter-wave or half-wave antennas because it would be impossible to build an antenna to exactly match the lower frequencies. This is a simple explanation, for a more detailed description, take a look at Wikipedia "Wavelength".  - This page last updated on 2 Sep 2017