3_1_Module2 Lecture Notes

3_1_Module2 Lecture Notes - EE3 Module 2: Logic and...

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EE3 Module 2: Logic and Computers The Binary Number System Why binary? It's easy to design electronic circuits with 2 states (high and low) Each digit in a binary number is a binary digit (or BIT) Each bit can take on only two values (1 and 0). Ex: Binary Decimal 0 0 1 1 10 2 11 3 100 4 101 5 110 6 111 7 1
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Decimal 153: 153d = 1*10 2 = 100 + 5*10 1 = 50 + 3*10 0 = 3 153 10011001b = 1*2 7 = 128 + 0*2 6 = 0 + 0*2 5 = 0 + 1*2 4 = 16 + 1*2 3 = 8 + 0*2 2 = 0 + 0*2 1 = 0 + 1*2 0 = 1 153 You should memorize the decimal equivalents of 2 0 - 2 16 2
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Logical Operations Circuits do simple logical operations. Combine circuits to do binary arithmetic and complex logical operations. We will use Truth Tables Shows all possible input values Shows corresponding outputs Let A and B take on 0 (FALSE) or 1 (TRUE) only. Ex: truth tables for AND, OR, NOT functions A B A B A B (AND) A+B A B (OR) Ā ¬A (NOT) 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 AND Gate: F = A B = A B OR Gate: F = A+B = A B 3
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NOT Gate: F= Ā =¬A NAND (NOT-AND) Gate: F = AB = A B NOR (NOT-OR) Gate: F = A B = A B XOR Gate: F=A B 4
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Boolean Algebra The symbol for AND is multiplication, but AND is not multiplication. The symbol for OR is addition, but OR is not addition. Commutative, associative, distributive laws work.
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This note was uploaded on 04/04/2010 for the course EE 3 taught by Professor Staff during the Winter '08 term at UCLA.

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3_1_Module2 Lecture Notes - EE3 Module 2: Logic and...

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