[Digital Logic] Magnitude Comparator | 절댓값 비교기

Magnitude Comparator

절댓값 비교기

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Specification

Inputs
\(A = a_3a_2a_1a_0\)
\(B = b_3b_2b_1b_0\)

Outputs
\((A = B) \mathrm{\;is\;} T/F\)

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Logic

\(A = a_3a_2a_1a_0\)
\(B = b_3b_2b_1b_0\)

\(x_i = a_ib_i + a_i'b_i' \qquad (\mathrm{for \;}i = 0, 1, 2, 3)\)

\(\mathrm{i.}   A = B\) \(\mathrm{Output\; =\; }x_3x_2x_1x_0\)

\(\mathrm{ii.}  A > B\) \(\mathrm{Output\; =\; }a_3b_3' + x_3a_2b_2' + x_3x_2a_1b_1' + x_3x_2x_1a_0b_0'\)

\(\mathrm{iii.} A < B\) \(\mathrm{Output\; = \;}a_3'b_3 + x_3a_2'b_2 + x_3x_2a_1'b_1 + x_3x_2x_1a_0'b_0\)

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Circuit Implementation