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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. TTL Fundamentals.

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bits bytes and nibbles

Bits, Bytes and Nibbles

Revision for A level year 2

ttl fundamentals
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
TTL Fundamentals
ttl fundamentals1
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
TTL Fundamentals
ttl fundamentals2
Further differences between analog and digital
  • Analog = amplification
  • Digital = switching
  • Analog = voltages
  • Digital = numbers
TTL Fundamentals
digital fundamentals
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
Digital Fundamentals
digital fundamentals1
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
Digital Fundamentals
digital fundamentals2
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
Digital Fundamentals
4 bit systems
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
4 bit systems
bits n pieces
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
Bits n pieces
binary representation1
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 Representation
binary code
Binary code can be read in series, where each bit follows one by one. This is known as serial transmissionBinary code
binary code1
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?
Binary code
decimal to binary conversion
Repeated division by 2
  • Convert 4610 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

Decimal to binary conversion
hexadecimal
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

Hexadecimal
binary to hex conversion
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
Binary to Hex conversion
hex to binary conversion
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
Hex to binary conversion
hex and 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
Hex and binary
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