Question 23 - Sample Paper 2 by Teachoo - Teachoo Sample Paper

Convert the octal number given below to hexadecimal number:

(7654) ₈

Answer:

Answer by student

The hexadecimal equivalent of the octal number (7654) ₈ is (F9C) ₁₆

Detailed answer by teachoo

To convert an octal number to a hexadecimal number, we need to follow these steps:

• Convert the octal number to a binary number by replacing each octal digit with its equivalent 3-bit binary representation. 
• Group the binary digits into groups of 4 bits from right to left. If the leftmost group has less than 4 bits, add leading zeros to make it 4 bits. 
• Convert each group of 4 bits to its equivalent hexadecimal digit by using the following table:

• Write the hexadecimal digits in the same order as the binary groups. For example, 0001 in binary is 1 in hexadecimal, 0101 in binary is 5 in hexadecimal, and so on.

Here is an example of how to convert (7654) ₈ to hexadecimal:

• Convert (7654) ₈ to binary by replacing each octal digit with its equivalent binary representation:

(7654) ₈ = (11111010100) ₂

• Group the binary digits into groups of 4 bits from right to left. Add leading zeros if necessary:

(11111010100) ₂ = (0001 1111 0101 00) ₂

• Convert each group of 4 bits to its equivalent hexadecimal digit using the table:

(0001) ₂ = (1) ₁₆

(1111) ₂ = (F) ₁₆

(0101) ₂ = (5) ₁₆

(00) ₂ = (0) ₁₆

• Write the hexadecimal digits in the same order as the binary groups:

(0001)(1111)(0101)(00) ₂ = (1)(F)(5)(0) ₁₆

• Remove any leading zeros from the hexadecimal number:

(10)(F)(5)(0) ₁₆ = (F50) ₁₆

So, the octal number (7654) ₈ is equivalent to the hexadecimal number (F50) ₁₆ .