Convert the number 3910 to binary

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Converting a decimal number, such as 39, to binary involves expressing the number in base-2 form. Binary is a positional numeral system with a base of 2, using only two digits: 0 and 1. Here's a detailed guide on how to convert the decimal number 39 to binary.

 

Binary Conversion Algorithm:

 

1. Divide by 2:

Divide the decimal number by 2.

 

2. Record Remainder:

Note down the remainder.

 

3. Update Quotient:

Update the quotient to be the result of the division.

 

4. Repeat:

Repeat steps 1-3 until the quotient becomes 0.

 

5. Read Backwards:

The binary equivalent is the sequence of remainders read backward.

 

Conversion of 39 to Binary:

Let's apply this algorithm to convert the decimal number 39 to binary:

1. \( 39 \div 2 = 19 \) with a remainder of 1. Record 1.

2. \( 19 \div 2 = 9 \) with a remainder of 1. Record 1.

3. \( 9 \div 2 = 4 \) with a remainder of 1. Record 1.

4. \( 4 \div 2 = 2 \) with a remainder of 0. Record 0.

5. \( 2 \div 2 = 1 \) with a remainder of 0. Record 0.

6. \( 1 \div 2 = 0 \) with a remainder of 1. Record 1.

Reading the remainders backward, the binary representation of 39 is 100111.

 

Checking the Result:

To verify the conversion, we can convert the binary representation back to decimal:

\[ 1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \

times 2^1 + 1 \times 2^0 = 32 + 4 + 2 + 1 = 39 \]

The result matches the original decimal number, confirming the accuracy of the conversion.

 

Conclusion:

Converting decimal numbers to binary follows a systematic process of division and remainder recording. Understanding this process allows for accurate and efficient conversion between different number systems. In the case of 39, its binary representation is 100111.

Frequently Asked Questions FAQ

How do you convert a number to binary?
Converting a number to binary involves expressing the number in base-2 form. The process generally includes repeated division by 2 and recording the remainders.Here's a step-by-step direct on how to change over a decimal number to twofold: Decimal to Parallel Change Calculation: 1. **Divide by 2:**    - Start by dividing the decimal number by 2. 2. **Record Remainder:**    - Record the remainder of the division (either 0 or 1). 3. **Update Quotient:**    - Update the quotient to be the result of the division. 4. **Repeat:**    - Repeat steps 1-3 until the quotient becomes 0. 5. **Read Backwards:**    - The binary equivalent is the sequence of remainders read backward. Example: Converting 27 to Binary: Let's illustrate the process by converting the decimal number 27 to binary: 1. \( 27 \div 2 = 13 \) with a remainder of 1. Record 1. 2. \( 13 \div 2 = 6 \) with a remainder of 1. Record 1. 3. \( 6 \div 2 = 3 \) with a remainder of 0. Record 0. 4. \( 3 \div 2 = 1 \) with a remainder of 1. Record 1. 5. \( 1 \div 2 = 0 \) with a remainder of 1. Record 1. Reading the remainders backward, the binary representation of 27 is 11011.

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