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 = 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 = 2 nbits

* 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 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 =

* 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 to hexadecimal * From the table 0001 = 1, 1111 = F * Therefore = 1F in hexadecimal * Convert to hex

* Convert 7EF8 to binary * From the table * 7 = 0111 * E = 1110 * F = 1111 * 8 = 1000 * Therefore 7EF8 = * 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