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# Chapter 2 - Part 1 - PPT - Mano & Kime - 2nd Ed

## Slide 2 Outline

Outline Hierarchical Design Technology Parameters Propagation Delay Delay Models Fan-out Cost Positive and Negative Logic Design Tradeoffs

## Slide 3 Combinational Circuits

Combinational Circuits A combinational logic circuit has: A set of m Boolean inputs, A set of n Boolean outputs, and n switching functions, each mapping the 2m input combinations to an output such that the current output depends only on the current input values A block diagram: m Boolean Inputs n Boolean Outputs Combinatorial Logic Circuit

## Slide 4 Hierarchical Design

Hierarchical Design To control the complexity of the function mapping inputs to outputs: Decompose the function into smaller pieces called blocks Decompose each block s function into smaller blocks, repeating as necessary until all blocks are small enough Any block not decomposed is called a primitive block The collection of all blocks including the decomposed ones is a hierarchy Example: 9-input parity tree (see next slide) Top Level: 9 inputs, one output 2nd Level: Four 3-bit odd parity trees in two levels 3rd Level: Two 2-bit exclusive-OR functions Primitives: Four 2-input NAND gates

## Slide 5 Hierarchy for Parity Tree Example

Hierarchy for Parity Tree Example B O X 0 X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 Z O 9-Input odd function (a) Symbol for circuit 3-Input odd function A 0 A 1 A 2 B O 3-Input odd function A 0 A 1 A 2 B O 3-Input odd function A 0 A 1 A 2 B O 3-Input odd function A 0 A 1 A 2 X 0 X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 Z O (b) Circuit as interconnected 3-input odd function blocks B O A 0 A 1 A 2 (c) 3-input odd function circuit as interconnected exclusive-OR blocks (d) Exclusive-OR block as interconnected NANDs Design requires: 4 X 2 X 4 = 32 2-input NAND gates

## Slide 6 Reusable Functions and CAD

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 Representative Computer-Aided Design Tools: Schematic Capture Logic Simulators Timing Verifiers Hardware Description Languages Verilog and VHDL Logic Synthesizers Integrated Circuit Layout

## Slide 7 Top-Down versus Bottom-Up

Top-Down versus Bottom-Up A top-down design proceeds from an abstract, high-level specification to a more and more detailed design by decomposition and successive refinement A bottom-up design starts with detailed primitive blocks and combines them into larger and more complex functional blocks Designs usually proceed from both directions simultaneously Top-down design answers: What are we building? Bottom-up design answers: How do we build it? Top-down controls complexity while bottom-up focuses on the details

## Slide 8 Integrated Circuits

Integrated Circuits Integrated circuit (informally, 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 integration) - fewer than 10 gates MSI (medium-scale integration) - 10 to 100 gates LSI (large-scale integration) - 100 to thousands of gates VLSI (very large-scale integration) - thousands to 100s of millions of gates

## Slide 9 Technology Parameters

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 Logic Levels the signal value ranges for 1 and 0 on the inputs and 1 and 0 on the outputs (see Figure 1-1 of textbook) Noise Margin the maximum external noise voltage superimposed on a normal input value that will not cause an undesirable change in the circuit 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

## Slide 10 Propagation Delay

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 (tPHL) and low-to-high (tPLH) output signal changes may have different propagation delays. High-to-low (HL) and low-to-high (LH) transitions are defined with respect to the output, not the input. An HL input transition causes: an LH output transition if the gate inverts and an HL output transition if the gate does not invert.

## Slide 11 Propagation Delay (continued)

Propagation Delay (continued) Propagation delays measured at the midpoint between the L and H values Adobe Systems =

## Slide 12 Propagation Delay Example

Propagation Delay Example Find tPHL, tPLH and tpd for the signals given IN (volts) OUT (volts) t (ns) 1.0 ns per division tPHL=1.4 tPLH=1.1 tpd=1.4

### Slide notes

tPHL = 1.4 ns, tPLH = 1.1 ns, tpd = 1.4 ns

## Slide 13 Delay Models

Delay Models Transport delay - a change in the output in response to a change on the inputs occurs after a fixed specified delay Inertial delay - similar to transport delay, except that if the input changes such that the output is to change twice in a time interval less than the rejection time, the output changes do not occur. Models typical electronic circuit behavior, namely, rejects narrow pulses on the outputs

## Slide 14 Delay Model Example

Delay Model Example A A B: Transport Delay (TD) Inertial Delay (ID) B Time (ns) 0 4 2 6 8 10 12 14 16 No Delay (ND) a b c d e Propagation Delay = 2.0 ns Rejection Time = 1 .0 ns

## Slide 15 Fan-out

Fan-out Fan-out can be defined in terms of a standard load Example: 1 standard load equals the load contributed by the input of 1 inverter. Transition time -the time required for the gate output to change from H to L, tHL, or from L to H, tLH The maximum fan-out that can be driven by a gate is the number of standard loads the gate can drive without exceeding its specified maximum transition time

## Slide 16 Fan-out and Delay

Fan-out and Delay The fan-out loading a gate s output affects the gate s propagation delay Example: One realistic equation for tpd for a NAND gate with 4 inputs is: tpd = 0.07 + 0.021 SL ns SL is the number of standard loads the gate is driving, i. e., its fan-out in standard loads For SL = 4.5, tpd = 0.07 + 0.021*4.5 = 0.165 ns

## Slide 17 Cost

Cost In an integrated circuit: The cost of a gate is proportional to the chip area occupied by the gate The gate area is roughly proportional to the number and size of the transistors and the amount of wiring connecting them Ignoring the wiring area, the gate area is roughly proportional to the gate input count So gate input count is a rough measure of gate cost If the actual chip layout area occupied by the gate is known, it is a far more accurate measure

## Slide 18 Positive and Negative Logic

Positive and Negative Logic The same physical gate has different logical meanings depending on interpretation of the signal levels. Positive Logic HIGH (more positive) signal levels represent Logic 1 LOW (less positive) signal levels represent Logic 0 Negative Logic LOW (more negative) signal levels represent Logic 1 HIGH (less negative) signal levels represent Logic 0 A gate that implements a Positive Logic AND function will implement a Negative Logic OR function, and vice-versa.

## Slide 19 Positive and Negative Logic (continued)

Positive and Negative Logic (continued) Given this signal level table: What logic function is implemented? Positive Logic (H = 1) (L = 0) Negative Logic (H = 0) (L = 1) 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 Input X Y Output L L L L H H H L H H H H

### Slide notes

Positive Logic: OR Negative Logic: GO TO NEXT SLIDE

## Slide 20 Positive and Negative Logic (continued)

Positive and Negative Logic (continued) Rearranging the negative logic terms to the standard function table order: Positive Logic (H = 1) (L = 0) Negative Logic (H = 0) (L = 1) 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 OR AND

### Slide notes

Negative Logic: AND

## Slide 21 Logic Symbol Conventions

Logic Symbol Conventions Use of polarity indicator to represent use of negative logic convention on gate inputs or outputs X CKT X Y Z Logic Circuit X L L H H Y L H L H Z L H H H Y Z Positive Logic Negative Logic X Y Z

## Slide 22 Design Trade-Offs

Design Trade-Offs Cost - performance tradeoffs Gate-Level Example: NAND gate G with 20 standard loads on its output has a delay of 0.45 ns and has a normalized cost of 2.0 A buffer H has a normalized cost of 1.5. The NAND gate driving the buffer with 20 standard loads gives a total delay of 0.33 ns In which if the following cases should the buffer be added? The cost of this portion of the circuit cannot be more than 2.5 The delay of this portion of the circuit cannot be more than 0.40 ns The delay of this portion of the circuit must be less than 0.30 ns and the cost less than 3.0 Tradeoffs can also be accomplished much higher in the design hierarchy Constraints on cost and performance have a major role in making tradeoffs

### Slide notes

1. No buffer 2. Use buffer 3. Irrelevant - buffer needed to satisfy delay constraint, but cannot satisfy cost constraint.

## Slide 23 Summary

Summary Hierarchical Design Technology Parameters Propagation Delay Delay Models Fan-out Cost Positive and Negative Logic Design Tradeoffs

# Table of Contents

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