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Bits, Bytes and Nibbles

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

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  1. Bits, Bytes and Nibbles Revision for A level year 2

  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

  3. 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

  4. Further differences between analog and digital • Analog = amplification • Digital = switching • Analog = voltages • Digital = numbers TTL Fundamentals

  5. 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

  6. 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

  7. 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

  8. This diagram shows how a 4 bit system could reproduce (a very rough version) of a sine wave A 4 bit system

  9. 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

  10. 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

  11. Binary representation

  12. 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

  13. Binary code can be read in series, where each bit follows one by one. This is known as serial transmission Binary code

  14. 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

  15. 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

  16. Convert the following decimal values to binary using repeated division by 2 • 255 • 124 • 39 Repeated division by 2

  17. 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

  18. 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

  19. 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

  20. 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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