1. Combinational Circuits
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EE 4271 VLSI Design, Fall 2010
Combinational Circuits

2. Overview Combinational Circuit Chip Design styles Full-custom design
Cell library based design
Programmable Logic Array
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Combinational Logic

3. Combinational Circuits
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Combinational Circuits
A combinational circuit consists of logic gates whose outputs, at any time, are determined by combining the values of the inputs.
For n input variables, there are 2n possible binary input combinations.
For each binary combination of the input variables, there is one possible output.
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Combinational Logic

4. Combinational Circuits (cont.)
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Combinational Circuits (cont.)
Hence, a combinational circuit can be described by:
A truth table that lists the output values for each combination of the input variables, or
m Boolean functions, one for each output variable.
Combinational
Circuit
n-inputs
m-outputs • • • • • •
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Combinational Logic

5. Combinational vs. Sequential Circuits
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Combinational vs. Sequential Circuits
Combinational circuits are memory-less. Thus, the output value depends ONLY on the current input values.
Sequential circuits consist of combinational logic as well as memory elements (used to store certain circuit states). Outputs depend on BOTH current input values and previous input values (kept in the storage elements).
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Combinational Logic

6. Combinational vs. Sequential Circuits
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Combinational vs. Sequential Circuits
Combinational
Circuit
n-inputs
m-outputs
(Depend only on inputs)
Combinational Circuit
n-inputs
m-outputs
Combinational
Circuit
Storage
Elements
Present
state
Next
state
Sequential Circuit
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Combinational Logic

7. Important Design Concepts
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Important Design Concepts
Modern digital design deals with various methods and tools that are used to design and verify complex circuits and systems.
Concepts:
Design Hierarchy
Computer-Aided-Design (CAD) tools
Hardware Description Languages (HDLs)
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Combinational Logic

8. 2017/4/16
Design Hierarchy
“Divide-and-Conquer” approach used to cope with the challenges of designing complex circuits and systems (many times in the order of millions of gates).
Circuit is broken into blocks, repetitively.
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Combinational Logic

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Design Hierarchy Example: 9-input odd function (for counting # of 1 in inputs)
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Combinational Logic

10. Why is Hierarchy useful?
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Why is Hierarchy useful?
Reduces the complexity required to design and represent the overall schematic of the circuit.
Reuse of blocks is possible. Identical blocks can be used in various places in a design, or in different designs.
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Combinational Logic

11. Reusable Functions and CAD
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Reusable Functions and CAD
Whenever possible, we try to decompose a complex design into common, reusable function blocks
These blocks are
verified and well-documented
placed in libraries for future use
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Combinational Logic

12. 2017/4/16
Integrated Circuits
Integrated circuit (a chip) is a semiconductor crystal (most often silicon) containing the electronic components for the digital gates and storage elements which are interconnected on the chip.
Terminology - Levels of chip integration
SSI (small-scale integrated) - fewer than 10 gates
MSI (medium-scale integrated) - 10 to 100 gates
LSI (large-scale integrated) to thousands of gates
VLSI (very large-scale integrated) - thousands to 100s of millions of gates
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Combinational Logic

13. Technology Parameters
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Technology Parameters
Specific gate implementation technologies are characterized by the following parameters:
Fan-in – the number of inputs available on a gate
Fan-out – the number of standard loads driven by a gate output
Cost for a gate - a measure of the contribution by the gate to the cost of the integrated circuit
Propagation Delay – The time required for a change in the value of a signal to propagate from an input to an output
Power Dissipation – the amount of power drawn from the power supply and consumed by the gate
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Combinational Logic

14. 2017/4/16
Propagation Delay
Propagation delay is the time for a change on an input of a gate to propagate to the output.
Delay is usually measured at the 50% point with respect to the H and L output voltage levels.
High-to-low falling and low-to-high rising delays.
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Combinational Logic

15. Propagation Delay Example
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Propagation Delay Example
IN (volts)
tPHL = 1.4 ns, tPLH = 1.1 ns, tpd = 1.25 ns
OUT (volts)
t (ns)
1.0 ns per division
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Combinational Logic

16. 2017/4/16
Chip Design Styles
Full custom - the entire design of the chip down to the smallest detail of the layout is performed
Expensive, its timing and power is hard to analyze
only for dense, fast chips with high sales volume
Standard cell - blocks have been design ahead of time or as part of previous designs
Intermediate cost
Less density and speed compared to full custom
Gate array - regular patterns of gate transistors that can be used in many designs built into chip - only the interconnections between gates are specific to a design
Lowest cost
Less density compared to full custom and standard cell
Prototype design
The base of FPGA
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Combinational Logic

17. Cell Libraries Cell - a pre-designed primitive block
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Cell Libraries
Cell - a pre-designed primitive block
Cell library - a collection of cells available for design using a particular implementation technology
Cell characterization - a detailed specification of a cell for use by a designer
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Combinational Logic

18. Cell Library Based Design Procedure
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Cell Library Based Design Procedure
Specification
Write a specification for the circuit if one is not already available
Formulation
Derive a truth table or initial Boolean equations that define the required relationships between the inputs and outputs, if not in the specification
Optimization
Draw a logic diagram or provide a netlist for the resulting circuit using ANDs, ORs, and inverters
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Combinational Logic

19. Cell Library Based Design Procedure
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Cell Library Based Design Procedure
Technology Mapping
Map the logic diagram to the implementation technology selected
Map to CMOS
Evaluation
Evaluate the timing and power
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Combinational Logic

20. Design Example Specification BCD to Excess-3 code converter
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Design Example
Specification
BCD to Excess-3 code converter
Transforms BCD code for the decimal digits to Excess-3 code for the decimal digits
BCD code words for digits 0 through 9: 4-bit patterns 0000 to 1001, respectively
Excess-3 code words for digits 0 through 9: 4-bit patterns consisting of 3 (binary 0011) added to each BCD code word
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Combinational Logic

21. Design Example (continued)
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Design Example (continued)
Formulation
Conversion of 4-bit codes can be most easily formulated by a truth table
Variables - BCD: A,B,C,D
Variables - Excess-3 W,X,Y,Z
Don’t Cares - BCD to 1111
Input BCD
Output Excess - 3
A B C D
WXYZ
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Combinational Logic

22. Design Example (continued)
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Design Example (continued) B C D A 1 3 2 4 5 7 6 12 13 15 14 8 9 11 10 X w z y x
Optimization
K-maps
W = A + BC + BD
X = C + D + B
Y = CD +
Z = B B C D D C D
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Combinational Logic

23. Design Example (continued)
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Design Example (continued)
Optimization (continued)
Multiple-level using transformations W = A + BC + BD X = C + D + B Y = CD + Z =
Perform extraction, finding factor:
T1 = C + D W = A + BT1 X = T1 + B Y = CD + Z = B C D B C D C D D
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Combinational Logic

24. Design Example (continued)
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Design Example (continued)
Technology Mapping
Map with a library containing inverters and 2-input NAND, and then map it to a CMOS based circuit A B C D W X Y Z
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Combinational Logic Z

25. Technology Mapping Example
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Technology Mapping Example
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Combinational Logic

26. Timing Analysis Use static timing analysis which has been covered.
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Combinational Logic

27. Transmission Gate Based Design - Multiplexer
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Transmission Gate Based Design - Multiplexer
“Selects” binary information from one of many input lines and directs it to a single output line.
Also know as the “selector” circuit,
Selection is controlled by a particular set of inputs lines whose # depends on the # of the data input lines.
For a 2n-to-1 multiplexer, there are 2n data input lines and n selection lines whose bit combination determines which input is selected.
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Combinational Logic

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Multiplexer (cont.)
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Combinational Logic

29. 2-to-1-Line Multiplexer
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2-to-1-Line Multiplexer
Since 2 = 21, n = 1
The single selection variable S has two values:
S = 0 selects input I0
S = 1 selects input I1
The equation:
Y = S’ I0 + SI1
The circuit:
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Combinational Logic

30. Example: 4-to-1 MUX - Cell Library Based Design
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Example: 4-to-1 MUX - Cell Library Based Design
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Combinational Logic

31. 4–to–1-Line Multiplexer using Transmission Gates
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4–to–1-Line Multiplexer using Transmission Gates
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Combinational Logic

32. 16-Apr-17
MUX as a Universal Gate
We can construct AND and NOT gates using 2-to-1 MUXs. Thus, 2-to-1 MUX is a universal gate.
z = 0x + 1x’ = x’
z = x1x0 + 0x0’ = x1x0
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Combinational Logic

33. Programmable Logic Array
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Programmable Logic Array
The set of functions to be implemented is first transformed to product terms
Since output inversion is available, terms can implement either a function or its complement
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Combinational Logic

34. Programmable Logic Array Example
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To implement
F1= A’B’C+A’BC’+AB’C’=(AB+AC+BC+A’B’C’)’
F2=AB+AC+BC
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Combinational Logic

35. Programmable Logic Array Example
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Fuse intact
Fuse blown 1 F 2 A B C 4 3
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Combinational Logic

36. Summary Three design styles Transmission gate based design
Full custom design
Gate library based design
PLA based design
Transmission gate based design
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Combinational Logic