Hexadecimal Number System (original) (raw)
Last Updated : 17 Dec, 2025
The Hexadecimal system is a base-16 number system that plays an important role in computing and digital systems. It uses sixteen symbols to represent values:
Digits (0 to 9) and the letters A to F, where A = 10, B = 11, and so on up to F = 15.
Place Value of Digits in the Hexadecimal Number System
The numbers in the hexadecimal number system have weightage in powers of 16. The power of 16 increases as the digit is shifted towards the left of the number. This is explained by the example as,
**Example: (AB12) 16
Place value of each digit in ****(AB12)** 16 is,
**= A×16 3 + B×16 2 + 1×16 1 + 2×16 0
Conversion from Hexadecimal to Other Number Systems
Conversion of a number system means conversion from one base to another. The following are the conversions of the Hexadecimal Number System to other Number Systems:
**Hexadecimal to Decimal Conversion:
To convert a hexadecimal number to decimal (base-10), multiply each digit by its corresponding power of 16 and sum the results.
**Example: To convert (8EB4)16 into a decimal value
**Follow the steps given below:
- **Step 1: Write the decimal values of the symbols used in the Hex number i.e. from A-F
- **Step 2: Multiply each digit of the Hex number with its place value. Starting from right to left i.e. LSB to MSB.
- **Step 3: Add the result of multiplication and the final sum will be the decimal number.
**Hexadecimal to Binary Conversion
Each hexadecimal digit corresponds to a 4-bit binary sequence. Convert each digit individually and combine.
**Example: (B2E)16 is to be converted to binary
**Follow the steps given below:
- **Step 1: Convert the Hex symbols into their equivalent decimal values.
- **Step 2: Write each digit of the Hexadecimal number separately.
- **Step 3: Convert each digit into an equivalent group of four binary digits.
- **Step 4: Combine these groups to form the whole binary number.
**Hexadecimal to Octal Conversion:
Convert hexadecimal to binary, group the binary digits into sets of three (right to left), and convert each group to its octal equivalent.
**Example: (B2E)16 is to be converted to hex
**Follow the steps given below:
- **Step 1: We need to convert the Hexadecimal number to Binary first. For that, follow the steps given in the above conversion.
- **Step 2: Now to convert the binary number to an Octal number, divide the binary digits into groups of three digits starting from right to left i.e. from LSB to MSB.
- **Step 3: Add zeros before MSB to make it a proper group of three digits(if required)
- **Step 4: Now convert these groups into their relevant decimal values.
Decimal to Hexadecimal Conversion
Divide the decimal number by 16 repeatedly, noting remainders, until the quotient is 0. Read remainders in reverse order, using A–F for 10–15.
**Related Articles:
Facts About Hexadecimal Numbers
- Hexadecimal is a number system with a base value of 16.
- Hexadecimal numbers use 16 symbols or digital values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
- A, B, C, D, E, and F represent 10, 11, 12, 13, 14, and 15 in single-bit form.
- If you see an "0x" as a Prefix, it indicates the number is in Hexadecimal. For example, 0x3A
- The position of each digit in a Hexadecimal number has a weight of 16 to the power of its position.
Solved Examples on Hexadecimal Number System
**Example 1: Convert Hexadecimal 1A5 to Decimal
**Solution:
Multiply First Digit (1) by 16 squared (256)
1×162 = 256
Multiply Second Digit (A, which is 10 in decimal) by 16 to the power of 1 (16)
10×161 = 160
Multiply Third Digit (5) by 16 to the power of 0 (1)
5×160 = 5
Adding the results,
1A5 = 1×162 +A×161 + 5×160
⇒ 1A5 = 1×162 + 10×161 + 5×160
⇒ 1A5 = 256 + 160 + 5 = 421
Decimal Equivalent of Hexadecimal number 1A5 is 421
**Example 2: Convert Decimal 315 to Hexadecimal.
**Solution:
Divide Decimal Number by 16
315÷16 = 19 with Remainder 11
The remainder (11) is represented as B in hexadecimal
Repeat the division with the quotient (19)
19÷16 = 1 with Remainder of 3
The remainder (3) is represented as 3 in hexadecimal
Hexadecimal Equivalent of Decimal Number 315 is 13B
**Example 3: Convert (1F7)16 to Octal.
**Solution:
**Step 1: Convert (1F7) 16 to decimal using the powers of 16:
(1F7)16 = 1 × 162 + 15 × 161 + 7 × 160
⇒ (1F7)16 = 1 × 256 + 15 × 16 + 7 × 1
⇒ (1F7)16 = 256 + 240 + 7
⇒ (1F7)16 = (503)10
**Step 2: Convert the decimal number (503) 10 to octal by dividing it by 8 until the quotient is 0
503 ÷ 8 = 62 with a remainder of 7
62 ÷ 8 = 7 with a remainder of 6
7 ÷ 8 = 0 with a remainder of 7
Arrange the remainder from bottom to top
Therefore, (1F7)16 is equivalent to (767)8 in octal
**Example 4: Convert (A7B)16 to decimal.
(A7B)16 = A × 162 + 7 × 161 + B × 160
⇒ (A7B)16 = 10 × 256 + 7 × 16 + 11 × 1 (convert symbols A and B to their decimal equivalents; A = 10, B = 11)
⇒ (A7B)16 = 2560 + 112+ 11
⇒ (A7B)16 = 2683
Therefore, the decimal equivalent of (A7B)16 is (2683)10.
Practice Questions on Hexadecimal Number System
**Question 1: Convert the hexadecimal number 2A to binary.
**Question 2: Convert the binary number 110110 to hexadecimal.
**Question 3: Add the hexadecimal numbers 1F and A3. Provide the result in hexadecimal.
**Question 4: Subtract the hexadecimal number B6 from D9. Provide the result in hexadecimal.
**Question 5: Multiply the hexadecimal number 7E by 3. Provide the result in hexadecimal.
Answer Key
1. 101010
2. 36
3.C2
4.23
5.17A