Higher Engineering Mathematics

92 NUMBER AND ALGEBRA

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 hexadeci-
mal symbol assigned to each group as above from
Table 10.2.
Hence 11100111101010012 =E7A9 16
To convert 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 16. 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, 110101102 =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, 11001112 = (^6716)
Problem 17. 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, 110011112 =CF 16
(b) Grouping bits in fours from the right gives:
(^0001) ︸︷︷︸
1
(^1001) ︸︷︷︸
9
(^1110) ︸︷︷︸
E
and assigning hexadecimal
symbols to each group gives as above from
Table 10.2.
Thus, 1100111102 =19E 16
Problem 18. Convert the following hexadec-
imal 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 19. Convert the following hexadec-
imal 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 45 Further problems on hexadec-
imal numbers
In Problems 1 to 4, convert the given hexa-
decimal numbers into their decimal equivalents.

1. E7 16 [231 10 ]2. 2C 16 [44 10 ]


2. 9816 [152 10 ]4. 2 F 116 [753 10 ]
   In Problems 5 to 8, convert the given decimal
   numbers into their hexadecimal equivalents.