Answer to Question #315988 in Discrete Mathematics for Pravin

Question

Convert the following hexadecimal numbers to decimal numbers.

a) DE5₁₆

b) 2AB.4₁₆

Answer 1

a) To convert hexadecimal number DE5 to decimal, we follow these two steps:

1. Start from one's place in DE5 : multiply ones place with $16^0$ , tens place with $16^1$ and so on from right to left.
2. Add all the product we got from step 1 to get the decimal equivalent of DE5.

Using the above steps, here is the work involved in the solution for converting DE5 to decimal number:

Decimal equivalent of

""5"=5\\cdot16^0=5"

Decimal equivalent of

""E"=14\\cdot16^1=224"

Decimal equivalent of

""D"=13\\cdot16^2=3228"

Decimal equivalent of

DE5₁₆ = 3328₁₀ + 224₁₀ + 5₁₀ = 3557₁₀

b) To convert hexadecimal number 2AB.4, we convert its integral and fractional part individually and then add them to get the equivalent decimal number.

In the fractional part of hexadecimal number, we multiply tenths place by $16^{-1}$.

Decimal equivalent of

""B"=11\\cdot16^0=11"

Decimal equivalent of

""A"=10\\cdot16^1=160"

Decimal equivalent of

""2"=2\\cdot16^2=512"

Decimal equivalent of

2AB₁₆ = 512₁₀ + 160₁₀ + 11₁₀ =683₁₀

Now we will convert the fractional part 0.4 to decimal form.

Decimal equivalent of

""4"=4\\cdot16^{-1}=0.25"

Here is the final answer, the hexadecimal number 2AB.4 converted to decimal is therefore equal to:

2AB.4₁₆= 683₁₀ + 0.25₁₀= 683.25₁₀