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Definitions. Schematic: A drawing of interconnected gates. Net: Wires at the same voltage (electrically connected) Netlist: A list of all the devices and connections in a schematic. Fan-in: The # of inputs to a gate. Fan-out: The # of loads the gate drives. 4.
Reduce the number of gates? Reduce the number of gate inputs? Reduce the number of cascaded levels of gates? 14 What is the optimal realization? How do we explore the tradeoffs? Logic minimization: Reduce number of gates and complexity Logic optimization: Maximize speed and/or minimize power CAD tools 15 Canonical forms Canonical forms
Building Functions: Logic Gates • NOT: • AND: • OR: • Logic Gates digital circuit that either allows a signal to pass through it or not. Used to build logic functions There are seven basic logic gates: AND, OR, NOT,
Use symbols: a * b, a + b, and a’ (in fact, a * b can be just ab). { Original: w = (p AND NOT(s) AND k) OR t. { New: w = ps’k + t. Spoken as “w equals p and s prime and k, or t” Or even just “w equals p s prime k, or t” s’ known as “complement of s”.
Be familiar with drawing and interpreting logic gate circuit diagrams involving one or more of the above gates. Complete a truth table for a given logic gate circuit. Write a Boolean expression for a given logic gate circuit. Draw an equivalent logic gate circuit for a given Boolean expression.
The basic logic gates are the inverter (or NOT gate), the AND gate, the OR gate and the exclusive-OR gate (XOR). If you put an inverter in front of the AND gate, you get the NAND gate etc. One of the common tool in specifying a gate function is the truth table.
1. What is mathematical logic about? • provide a uniform, unambiguous language for mathematics • make precise what a proof is • explain and guarantee exactness, rigor and certainty in mathematics • establish the foundations of mathematics B1 (Foundations) = B1.1 (Logic) + B1.2 (Set theory) N.B.: Course does not teach you to think ...
