1989 in Binary

The process of converting 1989 from decimal to binary involves dividing the number 1989 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 1989 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 1989 by 2 until getting 0 as the quotient is 11111000101. 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 11111000101. 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 11111000101 in binary is indeed 1989 in the decimal number system.

1989 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 1989 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 1989, 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, 1989. 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 1989. 1989 - 1024 = 965.

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, 965. So, the next largest power of 2 is 2⁹, which is less than or equal to 965. Now, we have to write 1 in the 2⁹ place. And then subtract 512 from 965. 965 - 512 = 453.

Step 4 - Repeat until remainder is 0: Continue identifying the next largest power of 2 and writing 1 in those places. Subtract until the remainder is 0.

Step 5 - Fill in with 0s: For unused place values, write 0. Now, by substituting the values, we get the binary representation of 1989 as 11111000101.

Grouping Method: In this method, we divide the number 1989 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 1989 by 2. 1989 / 2 = 994. Here, 994 is the quotient and 1 is the remainder.

Step 2 - Divide the previous quotient (994) by 2. 994 / 2 = 497. Here, the quotient is 497 and the remainder is 0.

Step 3 - Repeat the previous step. 497 / 2 = 248. Now, the quotient is 248, and 1 is the remainder.

Step 4 - Continue dividing until the quotient is 0.

Step 5 - Write down the remainders from bottom to top. Therefore, 1989 (decimal) = 11111000101 (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 1989. Since the answer is 2¹⁰, write 1 next to this power of 2. Subtract the value (1024) from 1989. So, 1989 - 1024 = 965. Find the largest power of 2 less than or equal to 965. The answer is 2⁹. So, write 1 next to this power. Continue the process until the remainder is 0. Final conversion will be 11111000101.

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, 1989 is divided by 2 to get 994 as the quotient and 1 as the remainder. Now, 994 is divided by 2. Here, we will get 497 as the quotient and 0 as the remainder. Dividing 497 by 2, we get 248 as the quotient and 1 as the remainder. Continue dividing until the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 1989, 11111000101.

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., 2¹⁰, 2⁹, 2^8, etc. Find the largest power that fits into 1989. 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.

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: We can memorize the binary forms for smaller numbers.
   
• 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
   
• Even and odd rule: Whenever a number is even, its binary form will end in 0. For example, 1988 is even, and its binary form ends in 0. If the number is odd, then its binary equivalent will end in 1. For example, the binary of 1989 is 11111000101.
   
• 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 before the remainder is considered.

• Remainder: The amount left over after division when one number does not divide the other exactly.