ABSTRACT
A · B + A · B · C using de Morgan’s laws. (5) 3. Use a Karnaugh map to simplify the Boolean
expression:
A · B · C + A · B · C + A · B · C + A · B · C (6)
4. A clean room has two entrances, each having two doors, as shown in Fig. R17.1. A warning bell must sound if both doorsA and B or doors C and D are open at the same time. Write down the Boolean expression depicting this occurrence, and devise a logic network to operate the bell using NANDgates only. (8)
In questions 5 to 9, the matrices stated are:
A = (−5 2
7 −8 )
B = (
1 6 −3 −4
)
C = ( j3 (1 + j2)
(−1 − j4) −j2 )
D = ⎛ ⎝ 2 −1 3−5 1 0
4 −6 2
⎞ ⎠ E =
⎛ ⎝−1 3 04 −9 2
−5 7 1
⎞ ⎠
5. Determine A × B (4) 6. Calculate the determinant of matrix C (4)
7. Determine the inverse of matrix A (4)
8. Determine E × D (9) 9. Calculate the determinant of matrix D (5)
10. Use matrices to solve the following simultaneous equations:
4x − 3y = 17 x + y + 1 = 0 (6)
11. Use determinants to solve the following simultaneous equations:
4x + 9y + 2z = 21 −8x + 6y − 3z = 41
3x + y − 5z = −73 (10) 12. The simultaneous equations representing the cur-
rents flowing in an unbalanced, three-phase, star-connected, electrical network are as follows:
2.4I1 + 3.6I2 + 4.8I3 = 1.2 −3.9I1 + 1.3I2 − 6.5I3 = 2.6 1.7I1 + 11.9I2 + 8.5I3 = 0
Using matrices, solve equations for I1, I2 and I3 (10)
