1100 in Binary

The process of converting 1100 from decimal to binary involves dividing the number 1100 by 2.

Here, it is getting 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 1100 to binary. In the last step, the remainder is noted down bottom side up, and that becomes the converted value.

For example, the remainders noted down after dividing 1100 by 2 until getting 0 as the quotient is 10001001100. 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 1100. 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 10001001100 in binary is indeed 1100 in the decimal number system.

1100 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 1100 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. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 2^9 = 512 2^10 = 1024 Since 1024 is less than 1100, we stop at 2^10 = 1024.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^10 = 1024. 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, 1100. Since 2^10 is the number we are looking for, write 1 in the 2^10 place. Now the value of 2^10, which is 1024, is subtracted from 1100. 1100 - 1024 = 76.

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, 76. So, the next largest power of 2 is 2^6, which is 64. Now, we have to write 1 in the 2^6 place. And then subtract 64 from 76. 76 - 64 = 12.

Step 4 - Repeat the process for remaining value: Now we find the largest power of 2 less than or equal to 12, which is 2^3 = 8. Write 1 in the 2^3 place, then subtract 8 from 12. 12 - 8 = 4. The next largest power of 2 that fits 4 is 2^2 = 4. So, write 1 in the 2^2 place and subtract 4 from 4. 4 - 4 = 0. We need to stop the process here since the remainder is 0.

Step 5 - Identify the unused place values: In the steps above, we wrote 1 in the 2^10, 2^6, 2^3, and 2^2 places. Now, we can just write 0s in the remaining places. Now, by substituting the values, we get: 0 in the 2^0 place 0 in the 2^1 place 1 in the 2^2 place 1 in the 2^3 place 0 in the 2^4 place 0 in the 2^5 place 1 in the 2^6 place 0 in the 2^7 place 0 in the 2^8 place 0 in the 2^9 place 1 in the 2^10 place

Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 1100 in binary. Therefore, 10001001100 is 1100 in binary.

Grouping Method: In this method, we divide the number 1100 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 1100 by 2. 1100 / 2 = 550. Here, 550 is the quotient and 0 is the remainder.

Step 2 - Divide the previous quotient (550) by 2. 550 / 2 = 275. Here, the quotient is 275 and the remainder is 0.

Step 3 - Divide the previous quotient (275) by 2. 275 / 2 = 137. Now, the quotient is 137, and 1 is the remainder.

Step 4 - Divide the previous quotient (137) by 2. 137 / 2 = 68. Here, the remainder is 1.

Step 5 - Continue dividing the quotient by 2 until the quotient is 0. 68 / 2 = 34, remainder 0. 34 / 2 = 17, remainder 0. 17 / 2 = 8, remainder 1. 8 / 2 = 4, remainder 0. 4 / 2 = 2, remainder 0. 2 / 2 = 1, remainder 0. 1 / 2 = 0, remainder 1.

Step 6 - Write down the remainders from bottom to top.

Therefore, 1100 (decimal) = 10001001100 (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 1100. Since the answer is 2^10, write 1 next to this power of 2. Subtract the value (1024) from 1100. So, 1100 - 1024 = 76. Find the largest power of 2 less than or equal to 76. The answer is 2^6. So, write 1 next to this power. Now, repeat the process until the remainder is 0. Final conversion will be 10001001100.

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, 1100 is divided by 2 to get 550 as the quotient and 0 as the remainder. Now, 550 is divided by 2. Here, we will get 275 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 1100, 10001001100.

Rule 3: Representation Method This rule also involves breaking down the number into powers of 2. Identify the powers of 2 and write them down in decreasing order, i.e., 2¹⁰, 2⁹, 2⁸, etc. Find the largest power that fits into 1100. 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 1100, we use 0s for unused powers and 1s for used powers in the breakdown.

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 1100.

Memorize to speed up conversions: We can memorize the binary forms for numbers 1 to 20. 1 → 1, 2 → 10, 3 → 11, 4 → 100, 5 → 101, 6 → 110, 7 → 111, 8 → 1000, 9 → 1001, 10 → 1010, ..., 20 → 10100.

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, 1100 is even, and its binary form is 10001001100. Here, the binary of 1100 ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 1101 (an odd number) is 10001001101. As you can see, the last digit here is 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.

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

• Quotient: The result of division, which may be used as the dividend in the next step of binary conversion.

• Remainder: The number left over after division, used to determine the binary digits in conversion.