M16_3_discussion1

M16_3_discussion1 - Ex2.41 Determine the sum of minterms...

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Discussion Note EEM16 Week1 1. Digital signal v.s. analog signal 2. Number system (i) (47) 10 = (?) 2 (ii) Ex. 2.13 (a) Determine the radix-16 representation of the integer whose radix-2 representation is 1001010100011110. Hint: partition the radix vector into groups of four bits and determine the radix digit values which are coded by each group using the binary code (b) Determine the radix-2 representation of the integer whose radix-8 representation is 3456 Hint: code each radix digit using the binary code and concatenate the resulting groups of three bits (c) Using the hints above give a procedure to convert from radix-2 to radix-2 k and vice versa 3. Boolean Algebra (i) DeMorgan’s Law (a + b)’ = a’b’ (ab)’ = a’ + b’ (ii) Ex 2.24 (a) a’b’ + ab + a’b = a’ + b (b) a’ + a(a’b+b’c)’ = a’ + b + c’ 4. Sum of minterms & product of maxterms (i)
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Unformatted text preview: Ex2.41 Determine the sum of minterms and product of maxterms that are equivalent to E(x,y,z) = x’ + x (x’y+y’z)’ Boolean Algebra + and · are binary operations, not integers. Think of + as “or” and · as “and” 0 · 0 = 0 0 · 1 = 0 AND | 0 1 OR | 0 1 1 · 1 = 1 0 | 0 0 0 | 0 1 0 + 0 = 0 1 | 0 1 1 | 1 1 0 + 1 = 1 1 + 1 = 1 Commutative a + b = b + a a · b = b · a Associative a + (b + c) = (a + b) + c a · (b · c) = (a · b) · c Distributive a + (b · c) = (a + b) · (a + c) a · (b + c) = (a · b) + (a · c) Precedence a + (b · c) = a + bc Identity elements 0 + a = a + 0 = a 1 · a = a · 1 = a Complement of a or NOT a = 1, a’ = 0 and if a = 0, a’ = 1 a + a’ = 1 a · a’ = 0 (a’)’ = a Simplification a + a’b = a + b a(a’ + b) = ab Absorption a + ab = a a(a + b) = a DeMorgan’s Law (a + b)’ = a’b’ (ab)’ = a’ + b’...
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This note was uploaded on 02/09/2011 for the course M 16 taught by Professor . during the Spring '10 term at UCLA.

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M16_3_discussion1 - Ex2.41 Determine the sum of minterms...

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