Digital Circuit Design and Language
Boolean Algebra and Gate Minimization
Chang, Ik JoonKyunghee University
Canonical Form
+ Sum of Min-term?
+ Product of Max-term?
f1 = Σ m(1,4,7)f2 = Σ m(3,5,6,7)
f1 = ∏M(0,2,3,5,6)f2 = ∏M(1,2,3,5)
SIMPLIFYING 6-VARIABLE FUNCITONPartial truth table for 6-variable function
G(A, B, C, D, E, F) = m0 + m2 + m3 + Em5 + Em7 + Fm9 + m11 + m15 (+ don’t care terms)
ABCDEF G ABCDEF G0000XX 1 1001X1 10001XX X 1010XX X0010XX 1 1011XX 10011XX 1 1101XX X01011X 1 1111XX 101111X 1
SIMPLIFICATION USING MAP-ENTERED VARIABLES
+ G = A'B' + ACD + E(A'D) + F(AD)+ In general, Function = MS0 + P1MS1 + P2MS2 + · · ·
• MS0 = Minimal Sum when All Variables are 0• MS1 = Minimal Sum when Variable P1=1, All Others 0• MS2 = Minimal Sum when Variable P2=1, All Others 0
STATIC HAZARDS+ Static 1-Hazard
• Output must be 1, but momentarily goes to 0 for some change in inputs and some combination of propagation delays
+ Static 0-Hazard• If output must be 0, but momentarily goes to 1 for
some change in inputs and some combination of propagation delays
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