Hexadecimal Number System Practice Questions

The hexadecimal number system is a number system that uses 16 symbols to represent numbers. It is also called the base-16 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

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