Higher Engineering Mathematics

Assign-03-H8152.tex 11/7/2006 12: 42 Page 114

Number and Algebra

Assignment 3

This assignment covers the material contained

in Chapters 9 and 11.

The marks for each question are shown in

brackets at the end of each question.

1. Use the method of bisection to evaluate the root
   of the equation:x^3 + 5 x=11 in the rangex= 1
   tox=2, correct to 3 significant figures. (12)


2. Repeat question 1 using an algebraic method of
   successive approximations. (16)


3. The solution to a differential equation associated
   with the path taken by a projectile for which the
   resistance to motion is proportional to the velocity
   is given by:

y= 2 .5(ex−e−x)+x− 25

Use Newton’s method to determine the value of

x, correct to 2 decimal places, for which the value

ofyis zero. (11)

4. Convert the following binary numbers to decimal
   form:
   (a) 1101 (b) 101101.0101 (5)


5. Convert the following decimal number to binary
   form:
   (a) 27 (b) 44.1875 (9)


6. Convert the following denary numbers to binary,
   via octal:
   (a) 479 (b) 185.2890625 (9)
   7. Convert
   (a) 5F 16 into its decimal equivalent
   (b) 132 10 into its hexadecimal equivalent
   (c) 110101011 2 into its hexadecimal equivalent
   (8)
   8. Use the laws and rules of Boolean algebra to
   simplify the following expressions:
   (a)B·

(

A+B

)

+A·B

(b)A·B·C+A·B·C+A·B·C+A·B·C (9)

9. Simplify the Boolean expression
   A·B+A·B·Cusing de Morgan’s laws. (5)


10. Use a Karnaugh map to simplify the Boolean
    expression:

A·B·C+A·B·C+A·B·C+A·B·C (8)

11. A clean room has two entrances, each having
    two doors, as shown in Fig. A3.1. A warning bell
    must sound if both doorsAandBor doorsCand
    Dare open at the same time. Write down the
    Boolean expression depicting this occurrence,
    and devise a logic network to operate the bell
    using NAND-gates only. (8)

C D

AB

Dust-free

area

Figure A3.1