Hexadecimal to Binary Conversion Examples
In the case of octal to binary conversion, we had used groups of 3 bits for conversion purposes. This was based on the concept that radix of octal system is 8 = 2^{3}. The exponent 3 formed the basis of 3bit group selection. Extending this principle, we use groups of 4 bits each the case of hex since its radix is 16 = 2^{4.}. Example 14 will illustrate the procedure of hex to binary conversion.
Example 14: Find the binary equivalent of the hex number E73.
Solution: For the desired conversion, we prepare Table 1.12 based on the principle described in the case of octal to binary conversion. Note that commas are used to identify the groups in the last row.
Table 1.12 HexBinary conversion
From Table 1.12, we get the desired answer:
Given hex number

E

7

3

Binary equivalent of hex in each column

1110

0111

0011

Binary equivalent of E73

1110,0111,0011 1010011

(E73)_{16} = (111001110011)_{2}
Binary to Hexadecimal Conversion Examples
In the case of octalbinary conversion, we had used 3bit groups. Following this concept, we use 4bit groups for hexbinary conversion. Example 15 will illustrate the procedure.
Example 15: Convert binary number 11110100010 into equivalent hex number.
Solution: To solve the given problem, we prepare Table 1.13. In this case also, we use commas to separate the 4bit groups and add padding bit (0) as the first bit in the first group of 111 to make it into a 4bit group.
Table 1.13 Binaryhex conversion
Table 1.13 Binaryhex conversion
Given binary number separated into 43bit groups

0111,1010,0010,0110
 
Bits in groups

0111

1010

0010

0110

Corresponding hexl numbers

7

A

2

6

Hex equivalent of the given binary number

7A26

From Table 1.13, we get the desired answer:
(111 1010 0010 0110)_{2} ≡ (7A26)_{16}
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