Bits, Bytes, Nibbles and Numbers
Numbers have bases.
It's the little number at the right and subscripted.
But what a difference. Bases are basically the number of fingers you have to count with.
Base 10 Decimal.
People generally have 10 fingers to count on and love base 10. Each of the columns in a number have a weight of 10. It's called Decimal.
We use the numbers 0123456789. Counting higher makes 10.
COLUMN VALUE || 100s | 10s | 1s ||
BASE 10 || 0 | 0 | 0 ||
DECIMAL || 9 | 9 | 9 ||
Base 2 Binary.
Programmers and Digital Engineers are slightly different.
Having limited intelligence it was decided that the membership could
only reliable count using one finger of each hand.
This task was to difficult.
After a brief discussion with a normal person, it was decided that one hand would be used for pointing.
The numbers that can be used are 01
This is the binary numbering system.
COLUMN VALUE || 128s| 64s | 32s | 16s | 8s | 4s | 2s | 1s ||
BASE 2 || 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 ||
BINARY || 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 ||
||---------NIBBLE--------|---------NIBBLE--------||
||--------------------BYTE-----------------------||
||--HEXADECIMAL NUMBER---|--HEXADECIMAL NUMBER---||
OCTAL NUMBER---|--OCTAL NUMBER---|--OCTAL NUMBER---||
Base 16 Hexadecimal
A Hexadecimal number uses 4 bits (Nibble) and can have 16 values.
It uses the numbers 0123456789ABCDEF.
Base 8 Octal
Toons only have 8 fingers and use the numbers 01234567. Some toons have worked on computers and like base 8 or Octal.
An Octal number uses 3 bits and can have 8 values.
A Byte is such a lovely number.
A toon can count the columns and a programmer can count the numbers.
A byte can have the decimal values of 0 to 255. That makes 256 different values.
A byte is used for everything. It's used to measure storage.
For example,
How many bytes a hard disk can hold. Typically measured in millions.
How much storage an image takes and how many bytes must be transferred to see it.
Counting in Binary.
Counting in Binary is the same as counting in Decimal.
Except there are only two numbers "0" and "1"
If you have "1" and want to count one more you must carry into the 2s column.
You have the Binary number 10 or Decimal 2.
You must again carry at the Decimal number 3 or 11 Binary. You carry into the 4s column.
COLUMN VALUE || 4s | 2s | 1s || DECIMAL EQUIVALENT
BASE 2 || | | 0 || 0
BINARY || | | 1 || 1
|| | 1 | 0 || 2
|| | 1 | 1 || 3
|| 1 | 0 | 0 || 4
|| 1 | 0 | 1 || 5
|| 1 | 1 | 0 || 6
|| 1 | 1 | 1 || 7
Converting from Binary to Decimal.
Add the column values of every column that contains a "1".
To convert the number 101 Binary to Decimal.
There is a "1" in the "4s" column and a "1" in the "1s" column. So "4+1" is "5"
Computer Busses.
Busses are how the computer talks to the various controller boards in them.
A Bus contains three parts.
The first part is the Data.
How wide the data bus is determines how much data can be transferred at a time.
This is typically 8 bits (a byte), 16 bits (two bytes) or 32 bits (four bytes).
It can easily be seen that the wider the data bus width the faster the data transfer.
The second part is Address
This determines how many different locations it is possible to store data at.
The third part is Control.
Much of the control is operated by the CPU (Central Processing Unit).
The CPU notifies the bus with control signals the type of operation (Read or Write).
In a Write operation data is transferred from the CPU to an address on the bus.
In a Read operation data is transferred from the addressed location to the CPU.
Control signals from the CPU tell the devices connected to the bus:
When the address is stable on the buss. When data is stable on the bus.
Or, in a read cycle when to put the data on the bus
Interrupt signals are sent to the CPU when something needs service.
The CPU stops what it is doing determines what needs service, services it and continues with what it was doing.
Another type of bus operation is Direct Memory Access (DMA).
Basically a device on the bus tells the CPU to shut up and takes control.
It then transfers it's data directly to or from memory, or other devices.
Some smarter computers allow DMA cycles to occur when the CPU is thinking.
