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Original 2026-01-01

Modified 2026-02-28

1 98 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 98 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 Since 128 is<a>greater than</a>98, we stop at 2⁶ = 64.

4 Step 2- Identify the largest power of 2: In the previous step, we stopped at 2⁶ = 64. 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, 98. Since 2⁶ is the number we are looking for, write 1 in the 2⁶ place. Now the value of 2⁶, which is 64, is subtracted from 98. 98 - 64 = 34.

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

6 Step 4- Identify the next largest power of 2: Now we look for the largest power of 2 that fits into 2. 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.

7 Step 5- Identify the unused place values: In the steps above, we wrote 1 in the 2⁶, 2⁵, and 2¹ places. Now, we can just write 0s in the remaining places, which are 2⁴, 2³, and 2⁰. 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 2³ place 0 in the 2⁴ place 1 in the 2⁵ place 1 in the 2⁶ place

8 Step 6- Write the values in reverse order: We now write the numbers upside down to represent 98 in binary. Therefore, 1100010 is 98 in binary.

9 Grouping Method: In this method, we divide the number 98 by 2. Let us see the step-by-step conversion.

10 Step 1- Divide the given number 98 by 2. 98 / 2 = 49. Here, 49 is the quotient and 0 is the remainder.

11 Step 2- Divide the previous quotient (49) by 2. 49 / 2 = 24. Here, the quotient is 24 and the remainder is 1.

12 Step 3- Repeat the previous step. 24 / 2 = 12. Now, the quotient is 12, and 0 is the remainder.

13 Step 4- Repeat the previous step. 12 / 2 = 6. Here, the quotient is 6 and the remainder is 0.

14 Step 5- Repeat the previous step. 6 / 2 = 3. Here, the quotient is 3 and the remainder is 0.

15 Step 6- Repeat the previous step. 3 / 2 = 1. Here, the quotient is 1 and the remainder is 1.

16 Step 7- 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.

17 Step 8- Write down the remainders from bottom to top. Therefore, 98 (decimal) = 1100010 (binary).