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Understanding Encoders and Magnitude Comparators for Efficient Digital Systems

Learn about priority encoders to resolve input ambiguity, prioritize inputs, and use don't-care conditions. Explore magnitude comparators for number comparison, design approaches, algorithms, and implementation methods.

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Understanding Encoders and Magnitude Comparators for Efficient Digital Systems

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  1. Encoders • The inverse function of a decoder

  2. Priority Encoder • resolve the ambiguity of illegal inputs • only one of the input is encoded • D3 has the highest priority • D0 has the lowest priority • X: don't-care conditions • V: valid output indicator

  3. Magnitude Comparator • The comparison of two numbers • outputs: A>B, A=B, A<B • Design Approaches • the truth table • 22n entries - too cumbersome for large n • use inherent regularity of the problem • reduce design efforts • reduce human errors

  4. Algorithm -> logic • A = A3A2A1A0 ; B =B3B2B1B0 • A=B if A3=B3, A2=B2, A1=B1and A1=B1 • equality: xi= AiBi+Ai'Bi' • (A=B) = x3x2x1x0 • (A>B) = A3B3'+x3A2B2'+x3x2A1B1'+x3x2x1 A0B0' • (A>B) = A3'B3+x3A2'B2+x3x2A1'B1+x3x2x1 A0'B0 • Implementation • xi = (AiBi'+Ai'Bi)'

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