Digital Integrated Circuits

• Integrated circuits (ICs) are the fundamental components of digital circuits
• ICs are small silicon semiconductor crystals with electronic components for digital gates
• Gates are interconnected inside the IC to form the required circuit
• An IC chip is mounted in a ceramic or plastic container with thin gold wires connecting it to external pins
• IC vendors provide catalogs with detailed descriptions of their ICs

IC Technology Advancements

• Technology improvements have increased the number of gates that can be placed on a single IC chip
• Small-scale integration (SSI) devices have less than 10 indepedent gates
• Medium-scale integration (MSI) devices contain around 10 to 200 gates and performs functions like decoding and adding
• Large-scale integration (LSI) devices have from 200 to a few thousand gates and include processors and memory
• Very-large-scale integration (VLSI) devices contain thousands of gates like memory arrays and microcomputer chips

Digital IC Classification

• Digital IC's are classified based on their logic operation and specific circuit technology
• Circuit technology is referred to as a digital logic family
• Each logic family has its own basic electronic circuit
• The basic circuit in each technology is a NAND, NOR, or inverter gate
• The electronic components used to construct the basic circuit dictates the technology's name
• Popular logic families include:
  • TTL (Transistor-Transistor Logic)
  • ECL (Emitter-Coupled Logic)
  • MOS (Metal-Oxide Semiconductor)
  • CMOS (Complementary Metal-Oxide Semiconductor)
• Integrated circuits are used to provide various digital components in computer systems

Common Combinational Circuits

• A combinational circuit is a set of interconnected gates where the output is only dependent on the current input
• The appearance of the input is immediately followed by the output, with only gate delays

How to Define a Combinational Circuit

• Truth table: Lists output for each possible input combination
• Graphical symbols: Depicts the interconnected layout of gates
• Boolean equations: Expresses each output signal as a Boolean function of input signals
• Combinational circuits do not use periodic clock signals nor have storage
• There are no feedbacks involved and the output at all time is dependent on the inputs provided.
• The name "combinational" comes from the combinations of logic gates used
• A combinational system's output depends only on the current input
• Combinational circuits include adders, multiplexers, demultiplexers, decoders, encoders, and comparators

Adders

• Binary addition differs from Boolean algebra by adding a potential carry term to the result
• Addition is the most common arithmetic operation performed by processors with hardware capable of performing addition
• Subtraction is performed by adding the subtrahend expressed in 2s or 1s compliment to the minuend
• Multiplication is repeated addition of multiplicand to itself by multiplier
• Division is repeated subtraction of divisor from dividend
• Addition can be represented in Boolean terms to produce a 1-bit sum and a carry bit
• A half adder is a digital arithmetic circuit that adds a pair of bits

Half Adder

• Half adders are simple, useful combinational logic circuits
• Half adders find the sum of two bits
• Sum can be found using the XOR operation and the carry using the AND operation
• Adder circuits give the basic capability to perform arithmetic operations
• A half adder adds two bits and produces a sum and carry output
• Half adders cannot be used to add more than two 1-bit numbers

Full Adder

• Full adders are created from half adders to process carry bits when we want to add n-bits along with a carry
• Two half adders make a full adder
• Set adders together so the carry from one adder is provided as input to the next
• A full adder adds 3 bits, producing a sum and carry bit
• Full adders can be connected in series
• The carry bit "ripples" from one adder to another; hence, named ripple-carry adder
• A ripple-carry adder starts its carry ripples with LSB to MSB
• Adding two n-bit numbers requires one half-adder and n-1 full adders

Decoders

• A decoder selects one of the output lines depending on the input pattern
• An n-input decoder has 2n outputs
• An encoder reverses a decoder: encoding input lines to a binary number for output
• In an n-to-2n decoder, the n-bit input data is output to 2n outputs
• The output line corresponding to the combination on the input lines will be 1 and all other outputs will be 0
• The outputs are numbered from 0 to (2n - 1)
• Decoders are useful for address decoding with an additional input line, a decoder can be used as a de-multiplexer

Code Converters

• Code converters translate an input code word into an output bit pattern corresponding to a new code word
• A decoder is a code converter that changes an n-bit code word into a 2n-bit code word

Encoders

• Encoders reverse the operation of decoders
• Encoders take input lines and generate a binary number as output
• An encoder generates an n-bit code word as a function of the combination of values on its input.
• At the maximum, there can be 2n inputs
• The design of an encoder is executed by first drawing a truth table
  • It shows the n-bit output needed for each of the 2n combinations of inputs
  • The circuit diagrams are then derived for each output bit
• The output of an encoder is valid as long as only one of the inputs is 1
• Encoders have a way to indicate when the output is valid so that the presence of invalid inputs can be conveyed
  • This is typically done by an additional output control line
  • An enable input can be incorporated into the logic

Multiplexers

• A multiplexer is a switch connecting one of several inputs to the output
• The multiplexer connects multiple inputs to a single output
• One of the inputs is selected and passed to the output at any given time
• A set of n control/selector inputs selects one of the 2n inputs that are connected to the output
• A 2-bit selection code is needed to select one of four possible inputs
  • This is implemented as two select lines labeled C1 and C0

4-to-1-line Multiplexer

• Receives information from one of its input lines and directs it to a single output line
• Selection is dependent on the data and n selection inputs
• A multiplexer is a digital circuit that selects one of several analog or digital input signals and forwards the selected input into a single line
• 4 line multiplexer: a total of 6 inputs for two selection inputs, four data lines, and one output
• Multiplexers use a function table to relate data inputs and the single output as a function of the selection inputs
• Multiplexers can be used to control signal and data routing
• This is exemplified in loading a Program Counter with potential input

De-multiplexers

• A de-multiplexer is the inverse function of a multiplexer;
  • Connects to only one of several outputs
  • Has only one input and several outputs
  • Connects the one input to one of the outputs depending on the combination of values on a set of control/select inputs
• There can be a maximum of 2n outputs when there are n control signals

Comparators

• Comparators can implement relational operations (=, <, >)
• Comparator outputs 1 if inputs match but implementing < and > is more involved than testing equality
  • Equality is established comparing bit by bit
  • Positional weights are needed when comparing for < and >

Sequential Circuits

• Sequential circuits based around the current and the previous input variables

• Combinational systems makes outputs based on variable input only

• Sequential can change its value with its current and its input

  • Has to "remember" their current state

• Employs feedback with memory

• Employs a periodic clock signal output, with the effect of input, and the previous output

• Sequential output is produced in sequence- clock enables and disables functioning

• Has feedback, employs memory elements

• Defining feature- output depends on both input values and former

  • Property gives the “memory" of sequential circuits

• Employs sequence of past input, and a set of state variables

  • In general, feedback feeds these variables to the input
    • Feedback is an interconnection of outputs and inputs to the input circuits
    • Can also be Flip-flops that remember, and store state information

Types of Sequential Circuits

• Synchronous: Outputs change only at specific times
• Asynchronous: Outputs change at any time
• Digital circuits can operate in synchronous or asynchronous mode
  • Asynchronous circuits are independent of each other, meaning one asynchronous circuit has no bearing on time versus another
    • Asynchronous is problematic as one output circuit works on input to multiple. One is NOT viable at the same time
  • Synchronous, the circuit changes state at the precisely defined instances
    • Clock signal is the time point, which the circuit can exist. This definition specifies how fast the circuit exists

Clock Signals

• Clock signals sequence of 1s and 0s
  • The clock at 1 state = "ON" period, 0 state = "OFF" period
• Symmetrical or unsymmetrical
• Clock provides Global Sync to entire system
• Cycle gives distinct start, end, and immediate point with signal changing level

Measuring Cycles

• When the clock is going from 0 to 1- the rising edge of the clock (positive)
• When the clock goes from 1 to zero- the falling edge (trailing, or negative)
• The time between the two successive rising edges is the clock cycle, the same if successive falling edges
  • It is measured in number of cycles per second, Hertz (Hz)
  • Millions of cycles per second: MHz
  • Length of clock- Clock period- Time represented by said level
• Change of state with a clock pulse- Edge triggered, by rising/falling edge cycle -Level trigerred- Clock reaches highest, or lowest level

Flip-Flops

• Simplest form of signal circuit
  • Storage used in clockwise, sequential circuits
  • Binary CELL capable of storing one bit of information
  • Has two outputs, value and complement
    • Maintains Binary state until directed at a clock pulse to switch states
  • Share two properties: Bistable device- two values, and when input is not present, it remains Two outputs that complement- labeled Q and Q_

S-R Flip-Flop

• The S-R latch employs two NOR Gates in sequence to implement SET-RESET logic

• The circuit is “bistable.”

• In one state, the output will oscillate between HI and LOW but will eventually settle. -In another state, the output will remain stable.

• SR Latch is very similar to the "Truth Table.“ it needs a characteristic Table displaying states + functions When BOTH HI, R and S not allowed in some models (inconsistent data where both equal 0)

• The ""Clocked"" SR flip-flop adjusts after brief timing, due to input Referred to as the ""asynchronous operation"" Events are more synchronized to clock pulse- changes occur in the clock pulse (below depicts arrangement) R + 0 = ""NOR"" gates during the loop pulse itself

D Flip-Flop

• The D flip-flop avoids the condition of SR = 11 input combo through one single input
• A gate setup + characteristic table with D flip flop- non clock inputs guarantee two AND Gates in opposite each other
• Data (D) Flip-Flop- storage for ONE bit -""The output of D: ALWAYS value -The most recent applies to input (remembers and produces the last input) -""Delay Flip Flop""- delays the clock pulse once applied

J–K Flip-Flop

• Inputs - Like SR FF. However in case input is valid- gate implementation by JK logic - The SNO. 51 = chart by that logic for SR and D’s FF
• Combinations are “Same” (but 3) for the SR FF’s, stable with UN-asserted input If ONLY asserted- Result = SET function, to BE one. IF ONLY-K input- result is RESET- function to be 0) Q. Which Is ONE + 1 AND J + K - = reverse (new value =0) referred as - the ""toggle function.""

Registers

• Registers are like storage units that can hold the binary data

Shift Registers

• A shift register operates by accepting, moving, or transferring information serially An example is a 5-bit shift construct, with clocked. With every cycle- data are shifted to the right- where bits are transferred out
• Interface to Serial I/O Devices (Shift Registers)
  • They can perform logic, shift, function, and rotate (ALU’s) but parallel circuit is needed

Counters

• The Counter Category- a circuit + function
  • Its number is easily added by the capacity (one is added via Modulo) -A register with a flip-flop can count TO and up for said number (power two, -1 from the value) -Clock that loads register -Designated asynchronous. or Synchronous -based on Operations -Asynchronous is slow based on flip flops triggering changes Synchronous counter can flip at the same time, so employed for CPUs

Types of Counters

• Ripple- Asynchronus- changes increment -""Ripples"" and ""move through"", and can add JK flippys- together a diagram of operations is idealized (DOES not show propogation- just the signals to move the series -Output of the FF- is the LSB (bit value, or 0 or 1) AND is for adding by cascading/ FF more -The counter is always the increment with every pulse from when constant -Synchronous counters
  • Have the disadvantage of ""Delay""
• CPUs + synchros can do it at the same time
• JK FFs are to ""Label"" the ""NO-completed Output AND 3 ff-"" -Create logic/ and truth states with JK table (the first section are from a -c), and the in order of- added/ increment ""JK inputs/AND outputs"", a table for circuit + use table AND ""add"" with karnuagh MAps- a map (expression where it derived- straight forward!""

Memory

• The memory of a computer system consists of tiny electronic switches, with each switch in one of two states: open or closed. It’s more convenient to think of states as 0 and 1 rather than Open and Closed

  • Thus
  • Each switch can represent a bit -The memory unit consists of millions of such bits, Eight bits are grouped to a byte to increase manageability A view of the computer consists of bytes with number starting with 0 -A memory is the address of said BUTE -Said address consists of two

• Random access memory (RAM): Random access to memory cells (for transfer) if need -The name signifies process is similar regardless of locatoin -RAM is made of sequential circuit components-Communicate + data, the address selection lines, and the controls ""N = data input"", n = output line ""k address= binary number k for bits"" / and is available in the memory

• Two controls show transfer desire. -Transfer in A ram can perform a write, a read, or in operation

ROM :ReadOnly Memory

• A combination can do memory less circuits cause outputs can only rely with the current input; no history -The name signifies process is similar regardless of location -To access information, the info + control is required! -To write address of choice the data bit -In conclusion. it’ll take any input bit+ place in word A given input on ROM given from address lines, to ALWAYS produce the same Data out Because it happens only at the one, the ""ROM"" (picture) - a ROM CAN BE COMPLETED with decoder + or gate (or table) look at table, its TRUTH- 4 in / AND 4 OUT! With given - to give a 64Bit from ROM. Specifying with: a 4, AND with outputs from section

Types of ROM

• In three ""Required Paths="" (rom's) it is coded in with multiple reasons Masks: 1: mask program does 1st -semiconductor last processing unit- must fill out with what it has must give. The form needs a special with instructions on a CD the manufacturer makes paths for 1 or 0, as CD provides
• ""COST"", is the change with vendor, it's great to CUSTOM masks - ROM! the machine should economical is what its is 2: Small qualities -""programmed"". ROM:
• A machine has intacted Fuses, for one, with Stored terms+ it BLOWN through by pulses from outputs for each address -A Blown: Equals 0 state. A machine- it, lets one programm by the ""own"" for achieve desired relationship to store terms -3: a third Rom avalible call - ERASABLE prom . restructred to ""Original"", even after fuse .when put under certain light, with the wave it discharge gates that are ""used"".
• after it get reset - can get a re-programmed terms AND (other promos can electrical- not wave)