1001 in Binary

The process of converting 1001 from decimal to binary involves dividing the number 1001 by 2.

Here, it is divided by 2 because the binary number system uses only 2 digits (0 and 1).

The quotient becomes the dividend in the next step, and the process continues until the quotient becomes 0.

This is a commonly used method to convert 1001 to binary.

In the last step, the remainder is noted down from bottom to top, and that becomes the converted value.

For example, the remainders noted down after dividing 1001 by 2 until getting 0 as the quotient is 1001.Remember, the remainders here have been written upside down.

In the table shown below, the first column shows the binary digits (1 and 0) as 1001.

The second column represents the place values of each digit, and the third column is the value calculation, where the binary digits are multiplied by their corresponding place values.

The results of the third column can be added to cross-check if 1001 in binary is indeed the correct representation of the decimal number.

1001 can be converted easily from decimal to binary. The methods mentioned below will help us convert the number. Let’s see how it is done.

Expansion Method: Let us see the step-by-step process of converting 1001 using the expansion method.

Step 1 - Figure out the place values: In the binary system, each place value is a power of 2. Therefore, in the first step, we will ascertain the powers of 2.

2⁰ = 1
2¹ = 2
2² = 4
2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
2⁸ = 256
2⁹ = 512

Since 512 is less than 1001, we stop at 2⁹ = 512.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2⁹ = 512. This is because in this step, we have to identify the largest power of 2, which is less than or equal to the given number, 1001. Since 2⁹ is the number we are looking for, write 1 in the 2⁹ place. Now the value of 2⁹, which is 512, is subtracted from 1001. 1001 - 512 = 489.

Step 3 - Identify the next largest power of 2: In this step, we need to find the largest power of 2 that fits into the result of the previous step, 489. The next largest power of 2 is 2⁸ = 256. Now, we have to write 1 in the 2⁸ places. And then subtract 256 from 489. 489 - 256 = 233.

Step 4 - Repeat the process for remaining values: 233 - 128 = 105 (2⁷ place), 105 - 64 = 41 (2⁶ place), 41 - 32 = 9 (2⁵ place), 9 - 8 = 1 (2³ place), 1 - 1 = 0 (2⁰ place). Now, by substituting the values, we get, 1 in the 2⁹ place, 1 in the 2⁸ place, 1 in the 2⁷ place, 1 in the 2⁶ place, 1 in the 2⁵ place, 0 in the 2⁴ place, 1 in the 2³ place, 0 in the 2² place, 1 in the 2¹ place, 1 in the 2⁰ place.

Step 5 - Write the values in order: We now write the numbers in order to represent 1001 in binary. Therefore, 1001 is 1001 in binary.

Grouping Method: In this method, we divide the number 1001 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 1001 by 2. 1001 / 2 = 500 with a remainder of 1.

Step 2 - Divide the previous quotient (500) by 2. 500 / 2 = 250 with a remainder of 0.

Step 3 - Repeat the previous step. 250 / 2 = 125 with a remainder of 0.

Step 4 - Repeat the previous step. 125 / 2 = 62 with a remainder of 1.

Step 5 - Repeat the previous step. 62 / 2 = 31 with a remainder of 0.

Step 6 - Repeat the previous step. 31 / 2 = 15 with a remainder of 1.

Step 7 - Repeat the previous step. 15 / 2 = 7 with a remainder of 1.

Step 8 - Repeat the previous step. 7 / 2 = 3 with a remainder of 1.

Step 9 - Repeat the previous step. 3 / 2 = 1 with a remainder of 1.

Step 10 - Repeat the previous step. 1 / 2 = 0 with a remainder of 1.

Step 11 - Write down the remainders from bottom to top. Therefore, 1001 (decimal) = 1111101001 (binary).

There are certain rules to follow when converting any number to binary. Some of them are mentioned below:

Rule 1: Place Value Method This is one of the most commonly used rules to convert any number to binary. The place value method is the same as the expansion method, where we need to find the largest power of 2. Let’s see a brief step-by-step explanation to understand the first rule. Find the largest power of 2 less than or equal to 1001. Since the answer is 2⁹, write 1 next to this power of 2. Subtract the value (512) from 1001. So, 1001 - 512 = 489. Find the largest power of 2 less than or equal to 489. The answer is 2⁸. So, write 1 next to this power. Now, 489 - 256 = 233. Continue this process until the remainder is 0. Final conversion will be 1111101001.

Rule 2: Division by 2 Method The division by 2 method is the same as the grouping method. A brief step-by-step explanation is given below for better understanding. First, 1001 is divided by 2 to get 500 as the quotient and 1 as the remainder. Now, 500 is divided by 2. Here, we will get 250 as the quotient and 0 as the remainder. Dividing 250 by 2, we get 125 as the quotient and 0 as the remainder. Continue this process until the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 1001, 1111101001.

Rule 3: Representation Method This rule also involves breaking the number into powers of 2. Identify the powers of 2 and write them down in decreasing order i.e., 2⁹, 2⁸, 2⁷, 2⁶, 2⁵, 2⁴, 2³, 2², 2¹, and 2⁰. Find the largest power that fits into 1001. Repeat the process and allocate 1s and 0s to the suitable powers of 2. Combine the digits (0 and 1) to get the binary result.

Rule 4: Limitation Rule The limitation of the binary system is that only 0s and 1s can be used to represent numbers. The system doesn’t use any other digits other than 0 and 1. This is a base 2 number system, where the binary places represent powers of 2. So, every digit is either a 0 or a 1. To convert 1001, we use a combination of 1s and 0s according to the powers of 2.

Learning a few tips and tricks is a great way to solve any mathematical problems easily. Let us take a look at some tips and tricks for binary numbers up to 1024.

Memorize to speed up conversions: We can memorize the binary forms for numbers up to 1024.

Recognize the patterns: There is a peculiar pattern when converting numbers from decimal to binary. 1 → 1 1 + 1 = 2 → 10 2 + 2 = 4 → 100 4 + 4 = 8 → 1000 8 + 8 = 16 → 10000 16 + 16 = 32 → 100000…and so on. This is also called the double and add rule.

Even and odd rule: Whenever a number is even, its binary form will end in 0. For example, 1001 is odd and its binary form ends in 1.

Cross-verify the answers: Once the conversion is done, we can cross-verify the answers by converting the number back to the decimal form. This will eliminate any unforeseen errors in conversion.

Practice by using tables: Writing the decimal numbers and their binary equivalents on a table will help us remember the conversions.

• Decimal: It is the base 10 number system which uses digits from 0 to 9.

• Binary: This number system uses only 0 and 1. It is also called the base 2 number system.

• Place value: Every digit has a value based on its position in a given number.

• Octal: It is the number system with a base of 8. It uses digits from 0 to 7.

• Hexadecimal: This number system has 16 digits. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Here, A to F represent the values 10 to 15.