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Bits, Bytes and Nibbles - PowerPoint PPT Presentation

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

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

TTL Fundamentals

• Further differences between following waysanalog and digital

• Analog = amplification

• Digital = switching

• Analog = voltages

• Digital = numbers

TTL Fundamentals

• So digital systems sample following waysanalog 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 following ways

• 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 Fundamentals

A 4 bit system

4 bit systems

Bits n pieces

Binary representation to the power of the number of bits.

• So to summarize to the power of the number of bits.

• 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

• Parallel transmission one by one. This is known as serial 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

• Repeated division by 2 one by one. This is known as serial transmission

• 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

Repeated division by 2

Because it is base 16, letters are used to represent the numbers in the upper register

• Convert 0001 1111 to hexadecimal numbers in base 16

• From the table 0001 = 1, 1111 = F

• Therefore 0001 1111 = 1F in hexadecimal

• Convert 0001 0101 1100 1110 to hex

Binary to Hex conversion

• Convert 7EF8 to binary numbers in base 16

• 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

• 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