162 in Binary
2026-02-28 17:39 Diff
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162 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 162 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 Since 256 is greater than 162, we stop at 2^7 = 128.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 27 = 128. 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, 162. Since 2^7 is the number we are looking for, write 1 in the 27 place. Now the value of 27, which is 128, is subtracted from 162. 162 - 128 = 34.

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, 34. So, the next largest power of 2 is 25 which is less than or equal to 34. Now, we have to write 1 in the 25 place. And then subtract 32 from 34. 34 - 32 = 2.

Step 4 - 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, 2. So, the next largest power of 2 is 21, which is equal to 2. Now, we have to write 1 in the 21 place. And then subtract 2 from 2. 2 - 2 = 0. We need to stop the process here since the remainder is 0.

Step 5 - Identify the unused place values: In steps 2, 3, and 4, we wrote 1 in the 27, 25, and 21 places. Now, we can just write 0s in the remaining places, which are 20, 22, 23, 24, and 26. Now, by substituting the values, we get: 0 in the 20 place 1 in the 21 place 0 in the 22 place 0 in the 2^3 place 0 in the 24 place 1 in the 2^5 place 0 in the 26 place 1 in the 27 place

Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 162 in binary. Therefore, 10100010 is 162 in binary.

Grouping Method: In this method, we divide the number 162 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 162 by 2. 162 / 2 = 81. Here, 81 is the quotient and 0 is the remainder.

Step 2 - Divide the previous quotient (81) by 2. 81 / 2 = 40. Here, the quotient is 40 and the remainder is 1.

Step 3 - Repeat the previous step. 40 / 2 = 20. Now, the quotient is 20, and 0 is the remainder.

Step 4 - Repeat the previous step. 20 / 2 = 10. Here, the quotient is 10, and 0 is the remainder.

Step 5 - Repeat the previous step. 10 / 2 = 5. Here, the quotient is 5, and 0 is the remainder.

Step 6 - Repeat the previous step. 5 / 2 = 2. Here, the quotient is 2, and 1 is the remainder.

Step 7 - Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1, and 0 is the remainder.

Step 8 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the division here because the quotient is 0.

Step 9 - Write down the remainders from bottom to top. Therefore, 162 (decimal) = 10100010 (binary).