Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 122 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 122 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>122, 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, 122. 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 122. 122 - 64 = 58.

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, 58. So, the next largest power of 2 is 2⁵ = 32. Now, we have to write 1 in the 2⁵ place. And then subtract 32 from 58. 58 - 32 = 26.

6 Step 4 -Identify the next largest power of 2: The next largest power of 2 that fits into 26 is 2⁴ = 16. Write 1 in the 2⁴ place. Then subtract 16 from 26. 26 - 16 = 10.

7 Step 5 -Identify the next largest power of 2: The next largest power of 2 that fits into 10 is 2³ = 8. Write 1 in the 2³ place. Then subtract 8 from 10. 10 - 8 = 2.

8 Step 6 -Identify the next largest power of 2: The next largest power of 2 that fits into 2 is 2¹ = 2. Write 1 in the 2¹ place. Then subtract 2 from 2. 2 - 2 = 0. We need to stop the process here since the remainder is 0.

9 Step 7 -Identify the unused place values: In steps 2, 3, 4, 5, and 6, we wrote 1 in the 2⁶, 2⁵, 2⁴, 2³, and 2¹ places. Now, we can just write 0s in the remaining places, which are 2² and 2⁰. Now, by substituting the values, we get, 0 in the 2⁰ place 1 in the 2¹ place 0 in the 2² place 1 in the 2³ place 1 in the 2⁴ place 1 in the 2⁵ place 1 in the 2⁶ place

10 Step 8 -Write the values in reverse order: We now write the numbers upside down to represent 122 in binary. Therefore, 1111010 is 122 in binary.

11 Grouping Method:In this method, we divide the number 122 by 2. Let us see the step-by-step conversion.

12 Step 1 -Divide the given number 122 by 2. 122 / 2 = 61. Here, 61 is the quotient and 0 is the remainder.

13 Step 2 -Divide the previous quotient (61) by 2. 61 / 2 = 30. Here, the quotient is 30 and the remainder is 1.

14 Step 3 -Repeat the previous step. 30 / 2 = 15. Now, the quotient is 15, and 0 is the remainder.

15 Step 4 -Repeat the previous step. 15 / 2 = 7. Here, the quotient is 7 and the remainder is 1.

16 Step 5 -Repeat the previous step. 7 / 2 = 3. Here, the quotient is 3 and the remainder is 1.

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

18 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.

19 Step 8 -Write down the remainders from bottom to top. Therefore, 122 (decimal) = 1111010 (binary).