Mechanical Engineering

Mechanical Engineering

Table of Contents
Activity 1:........................................................................................................................................1
Activity 2.........................................................................................................................................7
Activity 3.......................................................................................................................................12
Activity 4.......................................................................................................................................15
Activity 5.......................................................................................................................................16
Activity 6.......................................................................................................................................17
Activity 7.......................................................................................................................................18

Activity 1:
a) Conversion of numbers into binary, hexadecimal, octal and decimal equivalents
(i) 10101101112
Solution:
Binary to decimal:
= 1 x 29 + 0 x 28 + 1 x 27 + 0 x 26 + 1 x 25 + 1 x 24 + 0 x 23 + 1 x 22 + 1x 21 + 1 x 20
= 512 + 0 + 128 + 0 + 32 + 16 + 0 + 4 + 2 + 1
= 69510
Binary to octal:
10101101112 = 25678
Binary to hexadecimal:
So,
10101101112 = 2B78
(ii) 53278
1

Solution:
Octal to decimal:
= 5 x 83 + 3 x 82 + 2 x 81 + 7 x 80
= 5 x 512 + 3 x 64 + 2 x 16 + 7 x 1
= 279110
Octal to binary
53278 = 1010110101112
Octal to hexadecimal
53278 = 1010110101112
0111 = 7
1101 = D
1010 = A
So, 53278 = 7DA16
(iii) 429A16
Solution: A = 10
Hexadecimal to Octal:
429A16 =
4 – 0100
2 – 0010
9 – 1001
A – 1010
So, 100001010011010
Now, regrouping them –
100 – 4
001 – 1
010 – 2
011 – 3
010 – 2
So, 429A16 = 412328
Hexadecimal to Binary:
2

429A16 = 1000010100110102
Hexadecimal to decimal:
429A = 4 x 163 + 2 x 162 + 9 x 161 + 10 x 160
= 4 x 4096 + 2 x 256 + 9 x 16 + 10 x 1
= 16384 + 512 + 144 + 10
= 1705010
(iv) 1087510
Solution:
Decimal to Octal:
Decimal No Operation Quotient Remainder Octal Result
10875 ÷ 8 = 1359 3 3
1359 ÷ 8 = 169 7 73
169 ÷ 8 = 21 1 173
21 ÷ 8 = 2 5 25173
So, 1087510 = 251738
Decimal to Hexadecimal:
Decimal No Operation Quotient Remainder Hexadecimal Result
10875 ÷ 16 = 679 11 B
679 ÷ 16 = 42 7 7B
42 ÷ 16 = 2 10 A7B
So, 1087510 = 2A7B
Decimal to Binary:
Decimal No Operation Quotient Remainder Binary Result
10875 ÷ 2 = 5237 1 1
5237 ÷ 2 = 2618 1 11
2618 ÷ 2 = 1309 0 011
1309 ÷ 2 = 654 1 1011
654 ÷ 2 = 327 0 01011
327 ÷ 2 = 163 1 101011
163 ÷ 2 = 81 1 1101011
81 ÷ 2 = 40 1 11101011
3