Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 247 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 247 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. 20 = 1 21 = 2 22 = 4 23 = 8 24 = 16 25 = 32 26 = 64 27 = 128 28 = 256 Since 256 is<a>greater than</a>247, we stop at 27 = 128.

4 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<a>less than</a>or equal to the given number, 247. Since 27 is the number we are looking for, write 1 in the 27 place. Now the value of 27, which is 128, is subtracted from 247. 247 - 128 = 119.

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, 119. So, the next largest power of 2 is 26 = 64, which is less than or equal to 119. Now, we have to write 1 in the 26 places. And then subtract 64 from 119. 119 - 64 = 55.

6 Step 4- Repeat the process for remaining powers: Continue finding and subtracting the largest powers of 2 until reaching 0. 55 - 32 (25) = 23 23 - 16 (24) = 7 7 - 4 (22) = 3 3 - 2 (21) = 1 1 - 1 (20) = 0

7 Step 5- Write the values in reverse order: We now write the numbers upside down to represent 247 in binary. Therefore, 11110111 is 247 in binary.

8 Grouping Method: In this method, we divide the number 247 by 2. Let us see the step-by-step conversion.

9 Step 1- Divide the given number 247 by 2. 247 / 2 = 123. Here, 123 is the quotient and 1 is the remainder.

10 Step 2- Divide the previous quotient (123) by 2. 123 / 2 = 61. Here, the quotient is 61 and the remainder is 1.

11 Step 3- Repeat the previous step. 61 / 2 = 30. Now, the quotient is 30, and 1 is the remainder.

12 Step 4- Repeat the previous step. 30 / 2 = 15. Here, the quotient is 15 and 0 is the remainder.

13 Step 5- Continue the<a>division</a>until the quotient is 0. 15 / 2 = 7, remainder 1 7 / 2 = 3, remainder 1 3 / 2 = 1, remainder 1 1 / 2 = 0, remainder 1

14 Step 6- Write down the remainders from bottom to top. Therefore, 247 (decimal) = 11110111 (binary).