Universality, Gates, and Logic (Pdf)

Universality, Gates, and Logic (Pdf) - ESE534: Computer...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Penn ESE534 Spring2010 -- DeHon 1 ESE534: Computer Organization Day 2: January 20, 2010 Universality, Gates, Logic Work Preclass Exercise Penn ESE534 Spring2010 -- DeHon 2 Last Time • Computational Design as an Engineering Discipline • Importance of Costs Penn ESE534 Spring2010 -- DeHon 3 Today • Universality • Simple abstract computing building blocks – gates, Boolean Equations – RTL Logic (at least the logic part) • Logic in Gates – optimization – properties – Costs Preclass 1 • Do the Case 1 circuits calculate the same thing? • Case 2? Penn ESE534 Spring2010 -- DeHon 4 General • How do we define equivalence? – How do we determine if two circuits are equivalent? Penn ESE534 Spring2010 -- DeHon 5 Penn ESE534 Spring2010 -- DeHon 6 Model: Stateless Functions (Combinational Logic) • Compute some “ function – f(i 0 ,i 1 ,…i n ) o 0 ,o 1 ,…o m • Each unique input vector – implies a particular, deterministic, output vector
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Boolean Equivalence • Two functions are equivalent when – They have the same outputs for every input vector i.e. , they have the same truth table • There is a canonical specification for a Boolean function – its Truth Table Penn ESE534 Spring2010 -- DeHon 7 Penn ESE534 Spring2010 -- DeHon 8 Implementation in Gates Gate: small Boolean function Goal : assemble gates to cover our desired Boolean function • Collection of gates should implement same function I.e. collection of gates and Boolean function should have same Truth Table Penn ESE534 Spring2010 -- DeHon 9 Netlist Netlist: collection of interconnected gates – A list of all the gates and what they are connected to Implementation • How can I implement any Boolean function with gates? Penn ESE534 Spring2010 -- DeHon 10 Implementation • Single output {0, 1} – Use inverters to produce complements of inputs – For each input case (minterm) • If output is a 1 – Develop an AND to detect that case » Decompose AND into gates – OR together all such minterms • Decompose OR into gates • Multiple outputs – Repeat for each output Penn ESE534 Spring2010 -- DeHon 11 Universal set of primitives • What primitives did I need to support previous implementation set? Conclude: can implement any Boolean function by a netlist of gates selected from a small set. Homework (B.1): How small can set be? Penn ESE534 Spring2010 -- DeHon 12
Background image of page 2
3 Penn ESE534 Spring2010 -- DeHon 13 Boolean Equations • o=/a*/b*c+/a*b*/c+a*b*/c+a*/b*c • Another way to express Boolean functions a b c o 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 Penn ESE534 Spring2010 -- DeHon 14 Boolean Equations • o= /a*/b*c + /a*b*/c + a*b*/c + a*/b*c • Another way to express Boolean functions a b c o 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/04/2010 for the course ESE 534 taught by Professor Andredehon during the Spring '10 term at UPenn.

Page1 / 9

Universality, Gates, and Logic (Pdf) - ESE534: Computer...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online