Transcript Bits, Bytes and Nibbles

*
Revision for A level year 2
* TTL stands for Transistor Transistor Logic
* TTL operates on a power supply of 5 volts
* The power supply tolerance for TTL logic is less
than 10% ideally.
* TTL is used in digital electronics
* Digital systems are different from analogue systems
in the following ways
* Analog = Continuously variable voltage
* Digital = Discrete steps of voltage
* Think about climbing a hill
* A hill with no steps is analogous to analog
* A hill with steps cut out is analogous to digital
*
* Further differences between analog and digital
* Analog = amplification
* Digital = switching
* Analog = voltages
* Digital = numbers
*
* So digital systems sample analog voltages
* The value of each sample is stored as a number
* The sampling is carried out by an analog to digital
converter (ADC)
* The digital number can be stored in computer
memory either RAM or ROM
*
* Each digital number is stored in binary code
* Binary code is a system of representing
numbers using 1’s and 0’s
* In TTL systems a 1 = 2-5 volts = High = True
* In TTL systems a 0 = 0-0.8 volts = Low = False
*
* Each 1 or 0 which makes up a digital number is
known as a bit
* There are 8 bits in each byte
* There are 4 bits in each nibble
* The more bits that are used to take a sample of an
analog voltage the greater the accuracy of the
sample
*
* This diagram shows how a 4 bit system could
reproduce (a very rough version) of a sine wave
*
* Note the 4 bit system has 16 possible values
* You can find the maximum amount of values
any digital system can represent with the
equation:
* Maximum possible values = 2nbits
*
* So if the maximum amount of values available
is equal to 2 to the power of the number of
bits.
* Determine the maximum number of values that
can be represented by:
* An 8 bit system
* A 16 bit system
*
*
* So to summarize
* Any decimal number can be represented by a
binary code
* The more bits a system has the more numbers
that can be represented
* In electronic systems the bits are stored as
voltages
*
* Binary code can be read in series, where each
bit follows one by one. This is known as serial
transmission
*
* Parallel transmission
* This is where each bit of the code is
represented and transmitted at the same time,
not bit by bit as in serial
* Potentially it could be far quicker than serial
transmission but does suffer from one major
drawback. What do you think it could be?
*
* Repeated division by 2
* Convert 46 10 to binary
* Procedure
* 46/2 = 23 remainder 0 therefore LSB = 0
* 23/2 = 11 remainder 1 … second LSB = 1
* 11/2 = 5 remainder 1 …………………….= 1
* 5/2 = 2 remainder 1 …………………….= 1
* 2/2 = 1 remainder 0…………………….= 0
* 1/2 = 0 remainder 1…………… MSB = 1
Therefore 4610 = 1011102
*
* Convert the following decimal values to binary
using repeated division by 2
* 255
* 124
* 39
*
* Hexadecimal is a very convenient way of
representing binary numbers in base 16
Because it is
base 16, letters
are used to
represent the
numbers in the
upper register
*
* Convert 0001 1111 to hexadecimal
* From the table 0001 = 1, 1111 = F
* Therefore 0001 1111 = 1F in hexadecimal
* Convert 0001 0101 1100 1110 to hex
*
* Convert 7EF8 to binary
* From the table
* 7 = 0111
* E = 1110
* F = 1111
* 8 = 1000
* Therefore 7EF8 = 0111 1110 1111 1000
* Convert 8FAC to binary
*
* The most useful properties of the hexadecimal
system are the ability to store more digital
information in fewer digits and also as a shorthand
way of representing very large binary numbers.
* Once you have done a few conversions you will see
how easy it is
* Being comfortable with hexadecimal representation
will help greatly when you begin to work with
programming microcontrollers
*