Hexadecimal to Decimal Conversion Examples
Hexadecimal to decimal conversion is an essential concept in computer science, digital electronics, and number systems. It helps in converting compact base-16 numbers into standard base-10 numbers that are easier for humans to understand. This conversion is widely used in programming, memory addressing, color codes, and debugging.
What is Hexadecimal to Decimal Conversion?
Hexadecimal to decimal conversion is the process of converting a base-16 number into its equivalent base-10 number. Since hexadecimal uses digits from 0 to 9 and letters A to F (where A = 10, B = 11, …, F = 15), each digit is multiplied by powers of 16 based on its position.
Steps for Hexadecimal to Decimal Conversion
Hexadecimal to decimal conversion follows a positional value method. The step-by-step process is explained below:
- Write the given hexadecimal number
- Assign powers of 16 to each digit (starting from rightmost digit as 16⁰)
- Convert hexadecimal digits (A–F) into decimal values (10–15)
- Multiply each digit by its corresponding power of 16
- Add all the results
- The sum is the equivalent decimal number
Hexadecimal to Decimal Conversion Examples
Let’s explain 15 examples of hexadecimal to decimal conversion.
Example 1: Convert (1A3)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (1A3)₁₆ into its equivalent decimal number.
Description:
To convert (1A3)₁₆ into decimal, multiply each digit by its corresponding power of 16, starting from the rightmost digit (16⁰).
(1A3)₁₆ = 1×16² + A×16¹ + 3×16⁰
(1A3)₁₆ = 1×256 + 10×16 + 3×1
(1A3)₁₆ = 256 + 160 + 3
(1A3)₁₆ = (419)₁₀
Example 2: Convert (2F7)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (2F7)₁₆ into its equivalent decimal number.
Description:
To convert (2F7)₁₆ into decimal, multiply each digit by its corresponding power of 16, starting from the rightmost digit (16⁰).
(2F7)₁₆ = 2×16² + F×16¹ + 7×16⁰
(2F7)₁₆ = 2×256 + 15×16 + 7×1
(2F7)₁₆ = 512 + 240 + 7
(2F7)₁₆ = (759)₁₀
Example 3: Convert (ABC)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (ABC)₁₆ into its equivalent decimal number.
Description:
(ABC)₁₆ = A×16² + B×16¹ + C×16⁰
(ABC)₁₆ = 10×256 + 11×16 + 12×1
(ABC)₁₆ = 2560 + 176 + 12
(ABC)₁₆ = (2748)₁₀
Example 4: Convert (1A3F)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (1A3F)₁₆ into its equivalent decimal number.
Description:
(1A3F)₁₆ = 1×16³ + A×16² + 3×16¹ + F×16⁰
(1A3F)₁₆ = 1×4096 + 10×256 + 3×16 + 15×1
(1A3F)₁₆ = 4096 + 2560 + 48 + 15
(1A3F)₁₆ = (6719)₁₀
Example 5: Convert (3B2A)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (3B2A)₁₆ into its equivalent decimal number.
Description:
(3B2A)₁₆ = 3×16³ + B×16² + 2×16¹ + A×16⁰
= 3×4096 + 11×256 + 2×16 + 10×1
= 12288 + 2816 + 32 + 10
= (15146)₁₀
Example 6: Convert (7D4C1)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (7D4C1)₁₆ into its equivalent decimal number.
Description:
(7D4C1)₁₆ = 7×16⁴ + D×16³ + 4×16² + C×16¹ + 1×16⁰
= 7×65536 + 13×4096 + 4×256 + 12×16 + 1
= 458752 + 53248 + 1024 + 192 + 1
= (513217)₁₀
Example 7: Convert (9A7B3)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (9A7B3)₁₆ into its equivalent decimal number.
Description:
(9A7B3)₁₆ = 9×16⁴ + A×16³ + 7×16² + B×16¹ + 3×16⁰
= 9×65536 + 10×4096 + 7×256 + 11×16 + 3
= 589824 + 40960 + 1792 + 176 + 3
= (632755)₁₀
Example 8: Convert (1F2E9A)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (1F2E9A)₁₆ into its equivalent decimal number.
Description:
(1F2E9A)₁₆ = 1×16⁵ + F×16⁴ + 2×16³ + E×16² + 9×16¹ + A×16⁰
= 1×1048576 + 15×65536 + 2×4096 + 14×256 + 9×16 + 10
= 1048576 + 983040 + 8192 + 3584 + 144 + 10
= (2043546)₁₀
Example 9: Convert (ABCDE)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (ABCDE)₁₆ into its equivalent decimal number.
Description:
(ABCDE)₁₆ = A×16⁴ + B×16³ + C×16² + D×16¹ + E×16⁰
= 10×65536 + 11×4096 + 12×256 + 13×16 + 14
= 655360 + 45056 + 3072 + 208 + 14
= (703710)₁₀
Example 10: Convert (123ABC)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (123ABC)₁₆ into its equivalent decimal number.
Description:
(123ABC)₁₆ = 1×16⁵ + 2×16⁴ + 3×16³ + A×16² + B×16¹ + C×16⁰
= 1048576 + 131072 + 12288 + 2560 + 176 + 12
= (1194684)₁₀
Example 11: Convert (7F3A9C2)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (7F3A9C2)₁₆ into its equivalent decimal number.
Description:
(7F3A9C2)₁₆ = 7×16⁶ + F×16⁵ + 3×16⁴ + A×16³ + 9×16² + C×16¹ + 2
= 7×16777216 + 15×1048576 + 3×65536 + 10×4096 + 9×256 + 12×16 + 2
= 117440512 + 15728640 + 196608 + 40960 + 2304 + 192 + 2
= (133408,218)₁₀
Example 12: Convert (1ABCDE9)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (1ABCDE9)₁₆ into its equivalent decimal number.
Description:
(1ABCDE9)₁₆ = 1×16⁶ + A×16⁵ + B×16⁴ + C×16³ + D×16² + E×16¹ + 9
= 16777216 + 10485760 + 720896 + 49152 + 3328 + 224 + 9
= (280362,585)₁₀
Example 13: Convert (ABCDEF12)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (ABCDEF12)₁₆ into its equivalent decimal number.
Description:
(ABCDEF12)₁₆ = A×16⁷ + B×16⁶ + C×16⁵ + D×16⁴ + E×16³ + F×16² + 1×16¹ + 2
= 10×268435456 + 11×16777216 + 12×1048576 + 13×65536 + 14×4096 + 15×256 + 16 + 2
= (2882400018)₁₀
Example 14: Convert (123456789)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (123456789)₁₆ into its equivalent decimal number.
Description:
(123456789)₁₆ = 1×16⁸ + 2×16⁷ + 3×16⁶ + 4×16⁵ + 5×16⁴ + 6×16³ + 7×16² + 8×16¹ + 9
= 4294967296 + 536870912 + 50331648 + 4194304 + 327680 + 24576 + 1792 + 128 + 9
= (4886718345)₁₀
Example 15: Convert (1A2B3C4D5E)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (1A2B3C4D5E)₁₆ into its equivalent decimal number.
Description:
(1A2B3C4D5E)₁₆ = 1×16⁹ + A×16⁸ + 2×16⁷ + B×16⁶ + 3×16⁵ + C×16⁴ + 4×16³ + D×16² + 5×16¹ + E
= 68719476736 + 42949672960 + 536870912 + 184549376 + 3145728 + 786432 + 16384 + 3328 + 80 + 14
= (112394521,950)₁₀
2. Hexadecimal to Decimal Conversion of Fractional Numbers
Hexadecimal fractions can also be converted into decimal by using negative powers of 16. This method is important for handling precise values in computing, especially in graphics, memory representation, and scientific calculations.
- Start from the first digit after the decimal point
- Use powers like 16⁻¹, 16⁻², 16⁻³, …
- Convert A–F into 10–15
- Multiply and add the values
Example 1: Convert (1A.3F)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (1A.3F)₁₆ into its equivalent decimal number.
Description:
To convert a fractional hexadecimal number into decimal, convert the integer part using powers of 16 (16⁰, 16¹, …) and the fractional part using negative powers of 16 (16⁻¹, 16⁻², …).
(1A.3F)₁₆ = 1×16¹ + A×16⁰ + 3×16⁻¹ + F×16⁻²
= 16 + 10 + 0.1875 + 0.05859375
= (26.24609375)₁₀
Example 2: Convert (2F.4A)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (2F.4A)₁₆ into its equivalent decimal number.
Description:
(2F.4A)₁₆ = 2×16¹ + F×16⁰ + 4×16⁻¹ + A×16⁻²
= 32 + 15 + 0.25 + 0.0390625
= (47.2890625)₁₀
Example 3: Convert (7B.9C)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (7B.9C)₁₆ into its equivalent decimal number.
Description:
(7B.9C)₁₆ = 7×16¹ + B×16⁰ + 9×16⁻¹ + C×16⁻²
= 112 + 11 + 0.5625 + 0.046875
= (123.609375)₁₀
Example 4: Convert (A5.2E)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (A5.2E)₁₆ into its equivalent decimal number.
Description:
(A5.2E)₁₆ = A×16¹ + 5×16⁰ + 2×16⁻¹ + E×16⁻²
= 160 + 5 + 0.125 + 0.0546875
= (165.1796875)₁₀
Example 5: Convert (3C7.5D1)₁₆ to Decimal
Solution:
The following diagram shows the conversion of the hexadecimal number (3C7.5D1)₁₆ into its equivalent decimal number.
Description:
(3C7.5D1)₁₆ = 3×16² + C×16¹ + 7×16⁰ + 5×16⁻¹ + D×16⁻² + 1×16⁻³
= 768 + 192 + 7 + 0.3125 + 0.05078125 + 0.000244140625
= (967.363525390625)₁₀