lecture3-1

lecture3-1 - Bit Equality Generate 1 if a and b are equal...

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–1– Bit Equality Bit Equality ± Generate 1 if a and b are equal Bit equal a b f f(a,b) = (a&b)|(a’&b’) a b f(a,b) f(a,b) 0 0 1 0 1 0 1 0 0 1 1 1
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–2– Representation of Logic Functions Representation of Logic Functions A logic function can be represented as A logic function can be represented as ± a truth table ± a logic expression ± a logic circuit Example Example .c a a.d a.b.c .c a d) a.(b.c f + + = + + = a b c d f 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0
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–3– Forms of Boolean Expressions Forms of Boolean Expressions Sum Sum -of of -Products (SOP) form Products (SOP) form ± First the product terms (AND) are formed and then they are summed (OR) ± Eg. ABC+DEF+GHI Product Product -of of -Sums (POS) form Sums (POS) form ± First sums, then products. ± Eg (A+B+C).(D+E+F).(G+H+I) Interchange between 2 forms using Boolean Algebra. Interchange between 2 forms using Boolean Algebra. ± DeMorgan’s Law
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–4– SOP form SOP form f(a,b,c) = (a’.b.c) + (a.b’.c) + (a.b.c’) + (a.b.c)
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–5– Bit-Level Multiplexer Bit-Level Multiplexer ± Control signal s ± Data signals a and b ± Output a when s=1, b when s=0 Bit MUX b s a out out = (s&a)|(s’&b) s a b f(a,b,c) f(a,b,c) 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 Logic version of if-then-else statement
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This note was uploaded on 04/13/2008 for the course CS 211 taught by Professor Chakraborty during the Spring '08 term at Rutgers.

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lecture3-1 - Bit Equality Generate 1 if a and b are equal...

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