KFUPM COE 202: Digital Logic Design Number Systems Part 3 Courtesy of Dr. Ahmad Almulhem.
Digital Logic Design Review Dr. Ahmad Almulhem Email: ahmadsm AT kfupm Phone: 860-7554 Office:...
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Digital Logic DesignReview
Dr. Ahmad AlmulhemEmail: ahmadsm AT kfupm
Phone: 860-7554Office: 22-324
Ahmad Almulhem, KFUPM 2010
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Objectives
• Logic Circuits• Combinational
• Sequential
Ahmad Almulhem, KFUPM 2010
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Introduction
• Digital circuits have two classes:• Combinational Circuits• Sequential Circuits
• Combinational circuits consist of logic gates with inputs and outputs• The outputs at any instance of time depend only on
the combination of the input values based on logic operations such as AND, OR etc.
• Sequential circuits, in addition to inputs and outputs also have storage elements, therefore the output depends on both the current inputs as well as the stored values
Ahmad Almulhem, KFUPM 2010
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Combinational Circuits
Ahmad Almulhem, KFUPM 2010
CombinationalCircuits
..
..
InputX
OutputZ
Z = F(X)
In combinational circuits, the output at any time is a direct function of the applied external inputs
..
..
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Design Procedure of Combinational Circuits
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Circuit Specification
Truth TableHow many input/output?
Logic Diagram
MinimizationK-maps, Algebraic Manipulation. Computer based
tools
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Logic Gates
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AND OR
NAND NOR
XOR XNOR
NOT
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Physical Properties of Gates
• Building blocks of digital circuits• Built using integrated circuits• Integrated circuits themselves are built using various
technologies. E.g. TTL, CMOS• Physical characteristics of an Integrated Circuit depend
on the underlying technology• Key characteristics of ICs are:
• Physical voltage ranges for 1 and 0• Gate propagation delay/speed• Fan-in and Fan-out• Buffers• Tri-state Drivers
Ahmad Almulhem, KFUPM 2010
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Voltage Levels
• Logic values of 0 & 1 are represented in electrical terms using a voltage level
• A range of voltage defines logic 0 and logic 1.
• Any value outside this range is invalid.+5V
+0V
Illegal
Voltage Range
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Propagation Delay
• The delay when the voltage signal arrives at the input of a circuit, and when the output of the circuit changes, is called the propagation delay
• A circuit is considered to be fast, if its propagation delay is small (ideally as close to 0 as possible)
Delay between input (X, Y) and change in output Z
X
YZ
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Timing Diagram• The inputs to a circuit can be changed over time.
• The timing diagram shows the values of the input signals to a circuit with the passage of time, in the form of a waveform
• It also shows a waveform for the output
X
Y
Z
Propagation Delay of the Circuit = τ
Inputs
Output
Timing Diagram for an AND gate Time
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Fanin
• Fanin of a gate is the number of inputs to the gate
• For a 3-input OR gate, the fanin = 3
• There is a limitation on the fanin for any gate
• In CMOS IC technology, higher fanin implies slower gates (higher propagation delays)
• TTL IC gates can have higher fanin
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Fanout
• Fanout is the number of gates that can be driven by a driver gate
• The driven gate is called the load gate
• There is a limit to the number of load gates that can be driven by a driver gate
Fanout = 3
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Buffers
• Buffers have a single input and a single output, where output = input
• Buffers help increase the drive capability of a circuit by increasing the fanout
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Gates with Tristate outputs
• These gates have an additional input signal called the Enable
• This signal (Enable) if high, implies that inputs are accepted by the gate, and outputs are generated
• If Enable = 0, the gate is in a high impedance state, and the output is disabled
Enable
E X Z
1 0 0
1 1 1
0 0 High Z
0 1 High Z
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Decoder
• Information is represented by binary codes• Decoding - the conversion of an n-bit input code to
an m-bit output code with n <= m <= 2n such that each valid code word produces a unique output code
• Circuits that perform decoding are called decoders• A decoder is a minterm generator
Ahmad Almulhem, KFUPM 2010
..
.
.
n inputs 2n outputsn-to-2n
Decoder
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Decoder (Uses)
Decode a 3-bit op-codes: Home automation:
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3-to-8 Decoder
AddSubAndXorNotLoadStoreJump
op0op1op2 2-to-4
Decoder
LightA/CDoorLight-A/C
C0
C1
Load aAdd bStore c . .
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Decoder-Based Combinational Circuits (Example)
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Src: Mano’s book
X Y Z C S
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
S = ∑m (1,2,4,7)
C = ∑m (3,5,6,7)
3 inputs and 8 possible minterms3-to-8 decoder can be used for implementing this circuit
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Encoder
• Encoding - the opposite of decoding - the conversion of an m-bit input code to a n-bit output code with n m 2n such that each valid code word produces a unique output code
• Circuits that perform encoding are called encoders• An encoder has 2n (or fewer) input lines and n output lines
which generate the binary code corresponding to the input values
• Typically, an encoder converts a code containing exactly one bit that is 1 to a binary code corresponding to the position in which the 1 appears.
.
.
.
.
n outputs2n inputs2n-to-n
Encoder
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Multiplexers
• Is a combinational circuit
• Has a single output
• Directs one of 2n input to the output
• Input to output direction is done based on a set of n select bits
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2n inputs
n select lines
one output2n x 1
MUX
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MUX-based Design (n-1 Select lines)
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A B C F
0 0 0 0F = C
0 0 1 1
0 1 0 1F = C’
0 1 1 0
1 0 0 0F = 0
1 0 1 0
1 1 0 1F = 1
1 1 1 1
D0
D1
D2
D3
F
S1S0
A B
C
C’
0
1
F(A,B,C)=∑(1,3,5,6)
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Combinational vs Sequential
A combinational circuit:• At any time, outputs depends only on inputs
• Changing inputs changes outputs
• No regard for previous inputs• No memory (history)
• Time is ignored !
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CombinationalCircuits
inputs X outputs Z
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Combinational vs Sequential
A sequential circuit:• outputs depends on inputs and previous inputs
• Previous inputs are stored as binary information into memory
• The stored information at any time defines a state• next state depends on inputs and present state
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CombinationalCircuits
inputs X outputs Z
Memory
next statepresent state
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Examples of sequential systems
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Traffic light Vending machineATM
What is common between these systems?
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Types of Sequential Circuits
• Two types of sequential circuits:• Synchronous: The behavior of the circuit
depends on the input signal values at discrete intervals of time (also called clocked)
• Asynchronous: The behavior of the circuit depends on the order of change of the input signals at any instance of time (continuous)
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Design of Synchronous Sequential Circuits
• Obtain a state diagram• State reduction if necessary
• Obtain State Table• State Assignment• Choose type of flip-flops• Use FF’s excitation table to complete the table
• Derive state equations• Use K-Maps• Obtain the FF input equations and the output equations
• Draw the circuit diagram
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Building a Sequential Circuit
• Combinational part• Memory
• Latches
• Flip-Flops
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Flip Flops Sheet (Mano’s Textbook)
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Registers
• A register is a group of flip-flops.• An n-bit register is made of n flip-flips and can store n bits• A register may have additional combinational gates to
perform certain operations
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0 1 … n-1
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4-Bit Register
• A simple 4-bit register can be made with 4 D-FF
• Common Clock• At each positive-edge, 4 bits are
loaded in parallel
• Previous data is overwritten
• Common Clear• Asynchronous clear
• When Clear = 0, all FFs are cleared; i.e. 0 is stored.
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4-bit Shift Register
• A simple 4-bit shift register can be made with 4 D-FF• Common Clock
• At each positive-edge, 1 bit is shifted in• Rightmost bit is discarded
• Which direction this register is shifting?
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Universal Shift Register (cont.)
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Ripple Counters• Instead of having a common clock signal
to all Flip Flops, in a Ripple counter the output of one stage (Flip Flop) is connected to the clock input of the next stage
• T or JK flip flops are used for this construction because of their capability to flip their stored bits
• Clock is connected to the least significant bit
• Flip flops are negative edge-triggered (clock is bubbled) – are active when the clock signal is falling (high to low)
• Flip flops invert their stored bits, when the input clock signal goes from high (1) to low (0)
Ahmad Almulhem, KFUPM 2010
J
C
Q
Q’KR
J
C
Q
Q’KR
J
C
Q
Q’KR
J
C
Q
Q’KR
clock pulsesQ0
clear’
Q1
Q2
Q3
Logic 1
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Need more details ?
Ahmad Almulhem, KFUPM 2010
http://www.ccse.kfupm.edu.sa/~ahmadsm/teaching/coe202-092/coe202.html