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. RT18.1. A warning bell must sound if both doors A 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, starconnected, 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)

For lecturers/instructors/teachers, fully worked solutions to each of the problems in Revision Test 18, together with a full marking scheme, are available at the website:

www.routledge.com/cw/bird