Binary, octal and hexadecimal 95
symbols to each group gives as above from
Table 10.2.
Thus, 110011110 2 = 19E 16
(d) Converting from hexadecimal to binary:
The above procedure is reversed, thus, for example,
6CF3 16 = 0110 1100 1111 0011
from Table 10.2
i.e. 6CF3 16 = 110110011110011 2
Problem 22. Convert the following hexadecimal
numbers into their binary equivalents:
(a) 3F 16 (b) A6 16
(a) Spacing out hexadecimal digits gives:
3
0011
F
1111
and converting each into binary
gives as above from Table 10.2.
Thus, 3F 16 = 111111 2
(b) Spacing out hexadecimal digits gives:
A
1010
6
0110
and converting each into binary
gives as above from Table 10.2.
Thus, A6 16 = 10100110 2
Problem 23. Convert the following hexadecimal
numbers into their binary equivalents:
(a) 7B 16 (b) 17D 16
(a) Spacing out hexadecimal digits gives:
7
0111
B
1011
and converting each into binary
gives as above from Table 10.2.
Thus, 7B 16 = 1111011 2
(b) Spacing out hexadecimal digits gives:
1
0001
7
0111
D
1101
and converting each into
binary gives as above from Table 10.2.
Thus, 17D 16 = 101111101 2
Now try the following exercise
Exercise 43 Further problems on
hexadecimal numbers
In Problems 1 to 4, convert the given binary
numbers into their hexadecimal equivalents.
1. 11010111 2
[D7 16 ]
2. 11101010 2
[EA 16 ]
3. 10001011 2
[8B 16 ]
4. 10100101 2
[A5 16 ]
In Problems 5 to 8, convert the given hexadecimal
numbers into their binary equivalents.
5. 37 16
[110111 2 ]
6. ED 16
[11101101 2 ]
7. 9F 16
[10011111 2 ]
8. A21 16
[101000100001 2 ]