Binary11110101,decimalOctal,HEXADECIMALF5

The binary number `11110101` can be converted into decimal, octal, and hexadecimal as follows:

### 1. **Decimal Conversion:**
The binary number `11110101` can be converted to decimal by expanding it as a sum of powers of 2.

\[
11110101_2 = (1 \times 2^7) + (1 \times 2^6) + (1 \times 2^5) + (1 \times 2^4) + (0 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0)
\]

\[
= 128 + 64 + 32 + 16 + 0 + 4 + 0 + 1 = 245_{10}
\]

Thus, the **decimal value** of `11110101` is **245**.

### 2. **Octal Conversion:**
To convert the binary number to octal, group the binary digits in sets of 3 from the right (adding leading zeros if needed):

\[
111\ 101\ 01_2 = 011\ 110\ 101_2
\]

Convert each group to its octal equivalent:

\[
011_2 = 3,\ 110_2 = 6,\ 101_2 = 5
\]

Thus, the **octal value** of `11110101` is **365₈**.

### 3. **Hexadecimal Conversion:**
To convert the binary number to hexadecimal, group the binary digits in sets of 4 from the right:

\[
1111\ 0101_2
\]

Convert each group to its hexadecimal equivalent:

\[
1111_2 = F,\ 0101_2 = 5
\]

Thus, the **hexadecimal value** of `11110101` is **F5₁₆**.

---

Would you like further details or have any questions?

---

### Related Questions:
1. How do you convert from binary to other number systems in general?
2. What are the steps for converting decimal numbers into binary or hexadecimal?
3. What is the advantage of using hexadecimal representation in computing?
4. How are octal and hexadecimal representations used in programming?
5. Can you explain the relationship between octal and hexadecimal conversions?

### Tip:
When converting binary to hexadecimal, remember that every 4 binary digits correspond to one hexadecimal digit, making it a very efficient conversion.

Learn how to convert the binary number 11110101 to its decimal, octal, and hexadecimal equivalents. This detailed guide covers binary expansion for decimal conversion, grouping for octal and hexadecimal conversions, and is suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation