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Original 2026-01-01

Modified 2026-02-28

1 542 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.

2 Expansion Method:Let us see the step-by-step process of converting 542 using the expansion method.

3 Step 1 -Figure out the place values: In the binary system, each<a>place value</a>is a<a>power</a>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<a>2^5</a>= 32 2^6 = 64 2^7 = 128 2^8 = 256 2^9 = 512 Since 512 is<a>less than</a>542, we include 2^9.

4 Step 2 -Identify the largest power of 2: In the previous step, we identified 2^9 = 512 as the largest power of 2 less than or equal to 542. Write 1 in the 2^9 place. Now the value of 2^9, which is 512, is subtracted from 542. 542 - 512 = 30.

5 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, 30. The next largest power of 2 is 2^4 = 16, which fits into 30. Write 1 in the 2^4 place. Subtract 16 from 30. 30 - 16 = 14.

6 Step 4 -Repeat the process: The next largest power of 2 that fits into 14 is 2^3 = 8. Write 1 in the 2^3 place. Subtract 8 from 14. 14 - 8 = 6.

7 Step 5 -Continue the process: The next largest power of 2 that fits into 6 is 2^2 = 4. Write 1 in the 2^2 place. Subtract 4 from 6. 6 - 4 = 2.

8 Step 6 -Final step: The next largest power of 2 that fits into 2 is 2^1 = 2. Write 1 in the 2^1 place. Subtract 2 from 2. 2 - 2 = 0. We stop the process here since the remainder is 0.

9 Step 7 -Write the unused place values: Write 0s in the remaining places, which are 2^8, 2^7, 2^6, 2^5, and 2^0. Now, by substituting the values, we get: 0 in the 2^0 place 1 in the 2^1 place 1 in the 2^2 place 1 in the 2^3 place 1 in the 2^4 place 0 in the 2^5 place 0 in the 2^6 place 0 in the 2^7 place 0 in the 2^8 place 1 in the 2^9 place Therefore, 1000011110 is the binary representation of 542.

10 Grouping Method:In this method, we divide the number 542 by 2. Let us see the step-by-step conversion.

11 Step 1 -Divide the given number 542 by 2. 542 / 2 = 271. Here, 271 is the quotient and 0 is the remainder.

12 Step 2 -Divide the previous quotient (271) by 2. 271 / 2 = 135. Here, the quotient is 135 and the remainder is 1.

13 Step 3 -Repeat the previous step. 135 / 2 = 67. Now, the quotient is 67 and 1 is the remainder.

14 Step 4 -Repeat the previous step. 67 / 2 = 33. Here, the quotient is 33 and the remainder is 1.

15 Step 5 -Repeat the previous step. 33 / 2 = 16. Here, the quotient is 16 and the remainder is 1.

16 Step 6 -Repeat the previous step. 16 / 2 = 8. Here, the quotient is 8 and the remainder is 0.

17 Step 7 -Repeat the previous step. 8 / 2 = 4. Here, the quotient is 4 and the remainder is 0.

18 Step 8 -Repeat the previous step. 4 / 2 = 2. Here, the quotient is 2 and the remainder is 0.

19 Step 9 -Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1 and the remainder is 0.

20 Step 10 -Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the<a>division</a>here because the quotient is 0.

21 Step 11 -Write down the remainders from bottom to top. Therefore, 542 (decimal) = 1000011110 (binary).