ch 1 Intro to digital logic student version

ch 1 Intro to digital logic student version - EC262 Topic 2...

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1 EC262 Topic 2: Introduction to Combinational Systems Much of a computer’s hardware is comprised of digital logic circuits. Digital logic circuits are built from just a handful of primitive elements, called logic gates, combined in various ways. In a digital logic circuit, only two values may be present. The values may be 5 and + 5 volts. Or the values may be 0.5 and 3.5 volts. Or the values may be… you get the picture. To allow consideration of all of these possibilities, we will say that digital logic circuits allow the presence of two logical values: 0 and 1. So, signals in a digital logic circuit take on the values of 0 or 1. Logic gates are devices which compute functions of these binary signals. The Three Basic Logic Gates AND Gate . Consider the circuit below which has 2 switches in series: Switch S1 Switch S2 Light When will the light turn on? We can represent the light's operation using a table: S1 S2 Light open open off open shut off shut open off shut shut on Change the words open and off to 0 and the words shut and on to 1 and the table becomes S1 S2 Light This is the truth table for the AND operation. 0 0 0 0 1 0 1 0 0 1 1 1 The simplest AND gate gas two inputs and one output. If both inputs are 1 then the output is 1 . Otherwise, the output is 0 . The symbol for the AND gate is: We represent the AND operation by using either the multiplication symbol (i.e., “ “) or by writing the inputs together. Thus, for the AND gate above, we would write the output c as c ab = or as c = ab . This would be pronounced: “ C = a and b .”
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2 The truth table for the AND gate is shown below. The output c = ab is equal to 1 if and only if (iff) a is 1 and b is 1. Otherwise, the output is 0. a b c (Some textbooks use the symbol for the AND operation; i.e., some textbooks would use the notation cab = . We will not use this notation in this EC262, but you may see it in other classes in the future.) AND gates can have more than one input (however, an AND gate always has just a single output). Let’s consider a three-input AND gate: Write the expression for x : In words, how would you describe x ? Let’s write the truth table for the 3-input AND gate. Think: How many lines will be in a truth table with 3 inputs? Can you think of a way to present the table in an organized manner? OR Gate . Now consider the circuit that has 2 switches in parallel. Switch S1 Switch S2 Light When will the light turn on?
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3 We can represent the light's operation using a table S1 S2 Light open open off open shut on shut open on shut shut on Changing the words open and off to 0 and the words shut and on to 1 and the table becomes S1 S2 Light This is the truth table for the OR operation.
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This note was uploaded on 03/27/2012 for the course ECE 200 taught by Professor Nasis during the Spring '08 term at Drexel.

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ch 1 Intro to digital logic student version - EC262 Topic 2...

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