Decimal To Binary

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Convert Decimal to Binary: Decimal to Binary Converter

How can a decimal number be converted into binary? The decimal and binary systems are two of the most commonly used numeral systems in computing and electronics. Converting a decimal number to a binary number is an essential process in digital systems, allowing computers to encode values in a format they can process efficiently.

What is the Decimal Number System?

The decimal system (or base 10) uses digits from 0 to 9 to represent numbers. It is the standard system used for daily calculations and transactions.

What is the Binary Number System?

The binary number system (or base 2) consists of only two possible values: 0 or 1. Computers use this system because it aligns perfectly with digital circuits, which recognize only two states (on and off).

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How to Convert Decimal to Binary?

To convert a decimal number to binary, divide the number by 2 and record the remainders. These remainders form the binary digits (1 or 0), which are read in reverse order. This process reflects the power of 2, with each digit representing an increasing power of 2. For example, converting 1x to binary involves applying these steps.

What are the Rules to Convert Decimal to Binary?

Divide the decimal number by 2.
Write the remainder.
Repeat the process until the quotient becomes 0.
Read the remainders from bottom to top to get the binary equivalent.

Conversion Steps: Short Division by Two with Remainder

1. Divide the number by 2.

2. Write the remainder.

3. Repeat the process until you get 0.

4. Read the remainders in order (bottom to top).

Descending Powers of Two and Subtraction

Alternatively, you can subtract the largest powers of two from the decimal number to find its binary equivalent.

Example #1: Converting 10 to Binary

1. 10 ÷ 2 = 5, remainder = 0

2. 5 ÷ 2 = 2, remainder = 1

3. 2 ÷ 2 = 1, remainder = 0

4. 1 ÷ 2 = 0, remainder = 1

5. Binary equivalent of 10: 1010

Example #2: Converting 254 to Binary

1. 254 ÷ 2 = 127, remainder = 0

2. 127 ÷ 2 = 63, remainder = 1

3. 63 ÷ 2 = 31, remainder = 1

4. 31 ÷ 2 = 15, remainder = 1

5. 15 ÷ 2 = 7, remainder = 1

6. 7 ÷ 2 = 3, remainder = 1

7. 3 ÷ 2 = 1, remainder = 1

8. 1 ÷ 2 = 0, remainder = 1

9. Binary equivalent of 254: 11111110

Decimal to Binary Conversion Table

A Decimal to Binary Conversion Table shows how to convert the decimal into binary. It maps each decimal number to its binary digits, using the power of 2 for each place value.

What Does the Decimal to Binary Table Show?

It provides a quick reference for converting decimal values into their binary equivalents.

List the Decimal to Binary Values of the First Ten Decimal Numbers

Decimal Binary

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

Conversion of Decimal to Binary Examples

To convert a decimal number like 156 to binary, follow a step-by-step process. Divide the number by 2, recording the remainder (1's and 0's) for each step. The least significant bit is the rightmost bit, while the significant bit is the leftmost. Continue until you reach the dividend of 1. The result is a binary number in 32 bits or 16-bit format, representing the number's value in binary. For fractional numbers, the same method applies, considering the decimal point.

1. What is the Binary Equivalent of the Decimal Value 97?

97 in binary is 1100001.

2. What is 10 in Decimal to Binary?

10 in binary is 1010.

3. What is the Value of 34 in Binary?

34 in binary is 100010.

4. How Do You Convert 0.75 to Binary?

Multiply 0.75 by 2 → 1 (integer part) → 0.5 remains
Multiply 0.5 by 2 → 1 (integer part) → 0 remains
Binary equivalent of 0.75: 0.11

Decimal to Binary Practice Questions

1.What is 5 in Binary?

5 in binary is 101.

2. What is 13 in Binary?

13 in binary is 1101.

3. How to Convert Negative Decimal Numbers to Binary?

Negative numbers are represented using the sign bit or two’s complement notation.

Conversion Tools

1. Online Decimal to Binary Converter Tools

There are many free online calculators available to convert decimal numbers instantly.

2. Why Use a Decimal to Binary Converter?

Saves time
Reduces errors
Provides instant results

Final Thought:

In final thought, converting a decimal number like 156 to binary involves using step 1 to divide by 2, obtaining either 0 or 1 as the remainder. Each binary digit represents a power of 2 and reflects the value of 2. As you move to the next division, the significant bit and least significant bit are determined, creating a binary number that can be represented with 8 bits or even in hexadecimal format for simplicity. This method follows the same rules used in numeric systems like Hindu-Arabic and helps to represent decimal values accurately.

FAQs

How Do You Convert Decimal to Binary?

Use division by 2 and read the remainder in reverse order.

How is the Decimal to Binary Conversion Done?

It involves dividing the decimal number by 2 repeatedly and noting the remainder.

What is the Purpose of Converting Numbers from Decimal to Binary?

Computers operate on the binary system, making it essential to convert decimal numbers for digital processing.

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