Boolean Algebra. ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning. Inverter (Not Gate). If X = 0 then X' = 1 If X = 1 then X' = 0. AND Gate. If A = 1 and B = 1 then C = 1 (else C = 0). OR Gate. If A = 1 or B = 1 then C = 1 (else C = 0).
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Digital Logic and Circuits
Dr. Ron Hayne
Images Courtesy of Cengage Learning
Operations with 0 and 1:
1. X + 0 = X1D. X • 1 = X
2. X + 1 = 12D. X • 0 = 0
3. X + X = X3D. X • X = X
4. (X')' = X
Laws of complements:
5. X + X' = 15D. X • X' = 0
6. X + Y = Y + X 6D. XY = YX
7. (X + Y) + Z = X + (Y + Z) 7D. (XY)Z = X(YZ) = XYZ
8. X(Y+Z) = XY + XZ 8D. X + YZ = (X + Y)(X + Z)
9. (X + Y )' = X'Y' 12D. (XY)' = X' + Y'
10. XY+ XY' = X(Adjacency Theorem)
11. X + XY = X
AB'+ CD'E + AC'E'
(A + B')(C + D' + E)(A + C'+ E')