Digital Circuit Design and Language Boolean Algebra and Gate Minimization Chang, Ik Joon Kyunghee University
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