We will convert the binary number $(10111)_2$ into both decimal and hexadecimal.

Step 1: Convert Binary to Decimal

Each digit in a binary number represents a power of 2, starting from the right (least significant bit):

$(10111)_2 = 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0$

$= 1 \times 16 + 0 \times 8 + 1 \times 4 + 1 \times 2 + 1 \times 1$

$= 16 + 0 + 4 + 2 + 1 = 23$

So, $(10111)_2 = (23)_{10}$.

Step 2: Convert Decimal (23) to Hexadecimal

To convert $23_{10}$ to hexadecimal:

• Divide by 16:
  $23 \div 16 = 1 \text{ remainder } 7$

Thus, $(23)_{10} = (17)_{16}$.

Final Answer:

• Decimal: $(10111)_2 = (23)_{10}$
• Hexadecimal: $(10111)_2 = (17)_{16}$

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Would you like a detailed explanation of any step?

Here are five related questions for further learning:

1. How do you convert a decimal number to binary?
2. What is the binary representation of the hexadecimal number $2F$?
3. How can you quickly convert binary to hexadecimal?
4. What are the uses of binary and hexadecimal in computing?
5. How do you perform arithmetic operations in binary?

Tip: To convert binary to hexadecimal quickly, group the binary digits into sets of four from right to left and convert each group to its hexadecimal equivalent. 🚀