Data Representation: Hexadecimal to Binary Conversion

Objective

To convert between positive hexadecimal and positive binary representations.

Understanding Hexadecimal and Binary

Hexadecimal is a base-16 number system, using the digits 0-9 and A-F to represent values 0-15. Binary is a base-2 number system, using only the digits 0 and 1.

Conversion from Hexadecimal to Binary

Each hexadecimal digit corresponds to exactly four binary digits.

For example:

Hexadecimal 5 is equivalent to binary 0101.

Hexadecimal A is equivalent to binary 1010.

Method:

1. Identify each hexadecimal digit.
2. Convert each hexadecimal digit to its 4-bit binary equivalent.
3. Concatenate the binary equivalents of all hexadecimal digits to form the binary representation.

Example 1

Convert the hexadecimal number 2A to binary.

1. Hexadecimal 2 is 0010 in binary.
2. Hexadecimal A is 1010 in binary.
3. Concatenating these gives 00101010.

Therefore, the hexadecimal number 2A is equal to the binary number 00101010.

Example 2

Convert the hexadecimal number F3 to binary.

1. Hexadecimal F is 1111 in binary.
2. Hexadecimal 3 is 0011 in binary.
3. Concatenating these gives 11110011.

Therefore, the hexadecimal number F3 is equal to the binary number 11110011.

Table Summary

Hexadecimal	Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
A	1010
B	1011
C	1100
D	1101
E	1110
F	1111

Practice

Convert the following hexadecimal numbers to binary:

• 3C
• FF
• 1A

Note

Understanding the relationship between hexadecimal and binary is fundamental to data representation in computer science. This conversion is crucial for analyzing and manipulating data at a low level.