(10111)₂ convert binary to decimal and hexidecimal

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. 🚀

(10111)₂ convert binary to decimal and hexadecimal

Learn how to convert the binary number (10111)₂ to decimal and hexadecimal using step-by-step calculations. Understand the positional number system, key formulas, and methods for accurate conversion. Suitable for students in Grades 6-10.

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