94 Higher Engineering Mathematics
Problem 18. Convert the following decimal
numbers into their hexadecimal equivalents:
(a) 37 10 (b) 108 10
(a)
2 5
0
Remainder
5 5 5 16
2 5 2 16
16 2
16 37
least significant bit
most significant bit
Hence 37 10 = 25 16
(b)
6 C
0
Remainder
12 5 C 16
6 5 6 16
16 108
16 6
Hence 108 10 = 6C 16
Problem 19. Convert the following decimal
numbers into their hexadecimal equivalents:
(a) 162 10 (b) 239 10
(a)
A 2
0
Remainder
2 5 2 16
10 5 A 16
16 162
16 10
Hence 162 10 = A2 16
(b)
E F
0
Remainder
15 5 F 16
14 5 E 16
16 239
16 14
Hence 239 10 = EF 16
Now try the following exercise
Exercise 42 Further problems on
hexadecimal numbers
In Problems 1 to 4, convert the given hexadecimal
numbers into their decimal equivalents.
1. E7 16 [231 10 ]
2. 2C 16
[44 10 ]
3. 98 16 [152 10 ]
4. 2F1 16 [753 10 ]
In Problems 5 to 8, convert the given decimal
numbers into their hexadecimal equivalents.
5. 54 10 [36 16 ]
6. 200 10 [C8 16 ]
7. 91 10 [5B 16 ]
8. 238 10 [EE 16 ]
(c) Converting from binary to hexadecimal:
The binary bits are arranged in groups of four, starting from right to left, and a hexadecimal symbol is
assigned to each group. For example, the binary number 1110011110101001 is initially grouped in fours as:
1110
E
0111
7
1010
A
1001
9
and a hexadecimal symbol
assigned to each group as above from Table 10.2.
Hence 1110011110101001 2 = E7A9 16
Problem 20. Convert the following binary
numbers into their hexadecimal equivalents:
(a) 11010110 2 (b) 1100111 2
(a) Grouping bits in fours from the right gives:
1101
D
0110
6
and assigning hexadecimal symbols
to each group gives as above from Table 10.2.
Thus,
11010110 2 = D6 16
(b) Grouping bits in fours from the right gives:
0110
6
0111
7
and assigning hexadecimal symbols
to each group gives as above from Table 10.2.
Thus, 1100111 2 = 67 16
Problem 21. Convert the following binary
numbers into their hexadecimal equivalents:
(a) 11001111 2 (b) 110011110 2
(a) Grouping bits in fours from the right gives:
1100
C
1111
F
and assigning hexadecimal symbols
to each group gives as above from Table 10.2.
Thus, 11001111 2 = CF 16
(b) Grouping bits in fours from the right gives:
0001
1
1001
9
1110
E
and assigning hexadecimal
Problem 18. Convert the following decimal
numbers into their hexadecimal equivalents:
(a) 37 10 (b) 108 10
(a)
2 5
0
Remainder
5 5 5 16
2 5 2 16
16 2
16 37
least significant bit
most significant bit
Hence 37 10 = 25 16
(b)
6 C
0
Remainder
12 5 C 16
6 5 6 16
16 108
16 6
Hence 108 10 = 6C 16
Problem 19. Convert the following decimal
numbers into their hexadecimal equivalents:
(a) 162 10 (b) 239 10
(a)
A 2
0
Remainder
2 5 2 16
10 5 A 16
16 162
16 10
Hence 162 10 = A2 16
(b)
E F
0
Remainder
15 5 F 16
14 5 E 16
16 239
16 14
Hence 239 10 = EF 16
Now try the following exercise
Exercise 42 Further problems on
hexadecimal numbers
In Problems 1 to 4, convert the given hexadecimal
numbers into their decimal equivalents.
1. E7 16 [231 10 ]
2. 2C 16
[44 10 ]
3. 98 16 [152 10 ]
4. 2F1 16 [753 10 ]
In Problems 5 to 8, convert the given decimal
numbers into their hexadecimal equivalents.
5. 54 10 [36 16 ]
6. 200 10 [C8 16 ]
7. 91 10 [5B 16 ]
8. 238 10 [EE 16 ]
(c) Converting from binary to hexadecimal:
The binary bits are arranged in groups of four, starting from right to left, and a hexadecimal symbol is
assigned to each group. For example, the binary number 1110011110101001 is initially grouped in fours as:
1110
E
0111
7
1010
A
1001
9
and a hexadecimal symbol
assigned to each group as above from Table 10.2.
Hence 1110011110101001 2 = E7A9 16
Problem 20. Convert the following binary
numbers into their hexadecimal equivalents:
(a) 11010110 2 (b) 1100111 2
(a) Grouping bits in fours from the right gives:
1101
D
0110
6
and assigning hexadecimal symbols
to each group gives as above from Table 10.2.
Thus,
11010110 2 = D6 16
(b) Grouping bits in fours from the right gives:
0110
6
0111
7
and assigning hexadecimal symbols
to each group gives as above from Table 10.2.
Thus, 1100111 2 = 67 16
Problem 21. Convert the following binary
numbers into their hexadecimal equivalents:
(a) 11001111 2 (b) 110011110 2
(a) Grouping bits in fours from the right gives:
1100
C
1111
F
and assigning hexadecimal symbols
to each group gives as above from Table 10.2.
Thus, 11001111 2 = CF 16
(b) Grouping bits in fours from the right gives:
0001
1
1001
9
1110
E
and assigning hexadecimal