bits, bytes and nibbles
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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. - PowerPoint PPT PresentationTRANSCRIPT
Revision for A level year 2
*Bits, Bytes and Nibbles
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
*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
*Further differences between analog and digital
*Analog = amplification *Digital = switching*Analog = voltages*Digital = numbers
*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
*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
*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
*A 4 bit system
*This diagram shows how a 4 bit system could reproduce (a very rough version) of a sine wave
*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
*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
*Binary representation
*Binary Representation
*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
*Binary code can be read in series, where each bit follows one by one. This is known as serial transmission
*Binary code
*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?
*Decimal to binary conversion
*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
*Repeated division by 2
*Convert the following decimal values to binary using repeated division by 2*255*124*39
*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
*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
*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 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