# 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 = 23. The exponent 3 formed the basis of 3-bit group selection. Extending this principle, we use groups of 4 bits each the case of hex since its radix is 16 = 24.. 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 Hex-Binary conversion

 Given hex number E 7 3 Binary equivalent of hex in each column 1110 0111 0011 Binary equivalent of E73 1110,0111,0011  1010011

From Table 1.12, we get the desired answer:

(E73)16 = (111001110011)2

In the case of octal-binary conversion, we had used 3-bit groups. Following this concept, we use 4-bit groups for hex-binary 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 4-bit groups and add padding bit (0) as the first bit in the first group of 111 to make it into a 4-bit group.

Table 1.13 Binary-hex conversion

 Given binary number separated into 43-bit 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