1970 in Binary

The process of converting 1970 from decimal to binary involves dividing the number 1970 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 1970 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 1970 by 2 until getting 0 as the quotient is 11110110110. 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 11110110110.

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 11110110110 in binary is indeed 1970 in the decimal number system.

1970 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 1970 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 = 512 2¹⁰ = 1024 2¹¹ = 2048 Since 2048 is greater than 1970, we stop at 2¹⁰ = 1024.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2¹⁰ = 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, 1970. Since 2¹⁰ is the number we are looking for, write 1 in the 2¹⁰ place. Now the value of 2¹⁰, which is 1024, is subtracted from 1970. 1970 - 1024 = 946.

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, 946. So, the next largest power of 2 is 2⁹ = 512. Now, we have to write 1 in the 2⁹ places. And then subtract 512 from 946. 946 - 512 = 434.

Step 4 - Continue the process: Repeat the previous steps for the remaining number. 434 - 256 (2⁸) = 178 178 - 128 (2⁷) = 50 50 - 32 (2⁵) = 18 18 - 16 (2⁴) = 2 2 - 2 (2¹) = 0 Now, by substituting the values, we get, 0 in the 2⁰ place 1 in the 2¹ place 0 in the 2² place 1 in the 2³ place 1 in the 2⁴ place 0 in the 2⁵ place 1 in the 2⁶ place 0 in the 2⁷ place 1 in the 2⁸ place 1 in the 2⁹ place 1 in the 2¹⁰ place

Step 5 - Write the values in reverse order: We now write the numbers upside down to represent 1970 in binary. Therefore, 11110110110 is 1970 in binary.

Grouping Method: In this method, we divide the number 1970 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 1970 by 2. 1970 / 2 = 985. Here, 985 is the quotient and 0 is the remainder.

Step 2 - Divide the previous quotient (985) by 2. 985 / 2 = 492. Here, the quotient is 492 and the remainder is 1.

Step 3 - Repeat the previous step. 492 / 2 = 246. Now, the quotient is 246, and 0 is the remainder.

Step 4 - Repeat the previous step. 246 / 2 = 123. Here, the remainder is 0.

Step 5 - Continue until the quotient is 0. 123 / 2 = 61, remainder 1 61 / 2 = 30, remainder 1 30 / 2 = 15, remainder 0 15 / 2 = 7, remainder 1 7 / 2 = 3, remainder 1 3 / 2 = 1, remainder 1 1 / 2 = 0, remainder 1

Step 6 - Write down the remainders from bottom to top. Therefore, 1970 (decimal) = 11110110110 (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 1970. Since the answer is 2¹⁰, write 1 next to this power of 2. Subtract the value (1024) from 1970. So, 1970 - 1024 = 946. Find the largest power of 2 less than or equal to 946. The answer is 2⁹. So, write 1 next to this power. Continue this process until the remainder is 0, and fill in the place values with 0s and 1s accordingly. Final conversion will be 11110110110.

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, 1970 is divided by 2 to get 985 as the quotient and 0 as the remainder. Now, 985 is divided by 2. Here, we will get 492 as the quotient and 1 as the remainder. Continue dividing by 2 until the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 1970, 11110110110.

Rule 3: Representation Method

This rule also involves breaking of 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 1970. 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 1970, we use 0s and 1s for the various 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.

Memorize to speed up conversions: Memorize the binary forms for smaller numbers to gain efficiency.

Recognize the patterns: Binary numbers follow a pattern that can be understood with practice. 1 → 1 1 + 1 = 2 → 10 2 + 2 = 4 → 100 4 + 4 = 8 → 1000 8 + 8 = 16 → 10000

Even and odd rule: Whenever a number is even, its binary form will end in 0. For e.g., 1970 is even and its binary form is 11110110110. Here, the binary of 1970 ends in 0. If the number is odd, then its binary equivalent will end 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 that 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.

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

• Power of 2: In the binary system, each place value is a power of 2, which represents the base of the binary number system.