Higher Engineering Mathematics, Sixth Edition

Binary, octal and hexadecimal 95

symbols to each group gives as above from

Table 10.2.

Thus, 1100111102 =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 = (^1101100111100112)
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 = (^1111112)
(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 = (^101001102)
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 = (^11110112)
(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 = (^1011111012)
Now try the following exercise
Exercise 43 Further problems on
hexadecimalnumbers
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 ]