How do you convert 150 10 into binary then convert the binary number to octal?
2 Answers
Sure, let’s break it down step by step.
### Converting 150 (decimal) to binary:
1. **Divide the number by 2 and keep track of the remainders**:
- \( 150 \div 2 = 75 \) with a remainder of \( 0 \)
- \( 75 \div 2 = 37 \) with a remainder of \( 1 \)
- \( 37 \div 2 = 18 \) with a remainder of \( 1 \)
- \( 18 \div 2 = 9 \) with a remainder of \( 0 \)
- \( 9 \div 2 = 4 \) with a remainder of \( 1 \)
- \( 4 \div 2 = 2 \) with a remainder of \( 0 \)
- \( 2 \div 2 = 1 \) with a remainder of \( 0 \)
- \( 1 \div 2 = 0 \) with a remainder of \( 1 \)
2. **Write down the remainders in reverse order**:
- Binary representation of \( 150 \) is \( 10010110_2 \).
### Converting the binary number \( 10010110_2 \) to octal:
1. **Group the binary digits into sets of three, starting from the right**:
- \( 100 \, 101 \, 101 \, 10 \)
- Add leading zeros if necessary to make each group of three:
- \( 010 \, 010 \, 110 \)
2. **Convert each group of three binary digits to an octal digit**:
- \( 010_2 = 2_8 \)
- \( 010_2 = 2_8 \)
- \( 110_2 = 6_8 \)
So, the octal representation is \( 226_8 \).
### Summary
- Decimal \( 150_{10} \) is \( 10010110_2 \) in binary.
- Binary \( 10010110_2 \) is \( 226_8 \) in octal.
### Converting 150 (decimal) to binary:
1. **Divide the number by 2 and keep track of the remainders**:
- \( 150 \div 2 = 75 \) with a remainder of \( 0 \)
- \( 75 \div 2 = 37 \) with a remainder of \( 1 \)
- \( 37 \div 2 = 18 \) with a remainder of \( 1 \)
- \( 18 \div 2 = 9 \) with a remainder of \( 0 \)
- \( 9 \div 2 = 4 \) with a remainder of \( 1 \)
- \( 4 \div 2 = 2 \) with a remainder of \( 0 \)
- \( 2 \div 2 = 1 \) with a remainder of \( 0 \)
- \( 1 \div 2 = 0 \) with a remainder of \( 1 \)
2. **Write down the remainders in reverse order**:
- Binary representation of \( 150 \) is \( 10010110_2 \).
### Converting the binary number \( 10010110_2 \) to octal:
1. **Group the binary digits into sets of three, starting from the right**:
- \( 100 \, 101 \, 101 \, 10 \)
- Add leading zeros if necessary to make each group of three:
- \( 010 \, 010 \, 110 \)
2. **Convert each group of three binary digits to an octal digit**:
- \( 010_2 = 2_8 \)
- \( 010_2 = 2_8 \)
- \( 110_2 = 6_8 \)
So, the octal representation is \( 226_8 \).
### Summary
- Decimal \( 150_{10} \) is \( 10010110_2 \) in binary.
- Binary \( 10010110_2 \) is \( 226_8 \) in octal.
To convert the decimal number 150 to binary and then to octal, follow these steps:
### 1. Convert Decimal 150 to Binary
To convert a decimal number to binary, you repeatedly divide the number by 2 and keep track of the remainders. Here’s a step-by-step method:
1. **Divide the number by 2 and record the remainder.**
2. **Use the quotient from the previous division for the next division.**
3. **Repeat the process until the quotient is 0.**
4. **The binary number is the sequence of remainders read from bottom to top.**
Let’s apply this to 150:
1. **150 ÷ 2 = 75** with a remainder of **0**
2. **75 ÷ 2 = 37** with a remainder of **1**
3. **37 ÷ 2 = 18** with a remainder of **1**
4. **18 ÷ 2 = 9** with a remainder of **0**
5. **9 ÷ 2 = 4** with a remainder of **1**
6. **4 ÷ 2 = 2** with a remainder of **0**
7. **2 ÷ 2 = 1** with a remainder of **0**
8. **1 ÷ 2 = 0** with a remainder of **1**
Reading the remainders from bottom to top, the binary representation of 150 is **10010110**.
### 2. Convert Binary 10010110 to Octal
To convert a binary number to octal, follow these steps:
1. **Group the binary digits into sets of three, starting from the right.** If necessary, pad the leftmost group with zeros to ensure it contains three digits.
2. **Convert each group of three binary digits to its octal equivalent.**
Let’s apply this to the binary number 10010110:
1. Group the binary digits into sets of three from the right: **010 010 110**.
- If the number of digits isn't a multiple of 3, pad with zeros on the left. In this case, it is already grouped correctly.
2. Convert each group to octal:
- **010** (binary) = **2** (octal)
- **010** (binary) = **2** (octal)
- **110** (binary) = **6** (octal)
So, the binary number 10010110 converts to the octal number **226**.
### Summary
- Decimal 150 to binary: **10010110**
- Binary 10010110 to octal: **226**
### 1. Convert Decimal 150 to Binary
To convert a decimal number to binary, you repeatedly divide the number by 2 and keep track of the remainders. Here’s a step-by-step method:
1. **Divide the number by 2 and record the remainder.**
2. **Use the quotient from the previous division for the next division.**
3. **Repeat the process until the quotient is 0.**
4. **The binary number is the sequence of remainders read from bottom to top.**
Let’s apply this to 150:
1. **150 ÷ 2 = 75** with a remainder of **0**
2. **75 ÷ 2 = 37** with a remainder of **1**
3. **37 ÷ 2 = 18** with a remainder of **1**
4. **18 ÷ 2 = 9** with a remainder of **0**
5. **9 ÷ 2 = 4** with a remainder of **1**
6. **4 ÷ 2 = 2** with a remainder of **0**
7. **2 ÷ 2 = 1** with a remainder of **0**
8. **1 ÷ 2 = 0** with a remainder of **1**
Reading the remainders from bottom to top, the binary representation of 150 is **10010110**.
### 2. Convert Binary 10010110 to Octal
To convert a binary number to octal, follow these steps:
1. **Group the binary digits into sets of three, starting from the right.** If necessary, pad the leftmost group with zeros to ensure it contains three digits.
2. **Convert each group of three binary digits to its octal equivalent.**
Let’s apply this to the binary number 10010110:
1. Group the binary digits into sets of three from the right: **010 010 110**.
- If the number of digits isn't a multiple of 3, pad with zeros on the left. In this case, it is already grouped correctly.
2. Convert each group to octal:
- **010** (binary) = **2** (octal)
- **010** (binary) = **2** (octal)
- **110** (binary) = **6** (octal)
So, the binary number 10010110 converts to the octal number **226**.
### Summary
- Decimal 150 to binary: **10010110**
- Binary 10010110 to octal: **226**