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Original 2026-01-01

Modified 2026-02-28

1 123 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 123 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 Since 128 is<a>greater than</a>123, we stop at 2^6 = 64.

4 Step 2 -Identify the largest power of 2: In the previous step, we stopped at 2^6 = 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, 123. Since 2^6 is the number we are looking for, write 1 in the 2^6 place. Now the value of 2^6, which is 64, is subtracted from 123. 123 - 64 = 59.

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, 59. So, the next largest power of 2 is 2^5 = 32. Now, we have to write 1 in the 2^5 place. And then subtract 32 from 59. 59 - 32 = 27.

6 Step 4 -Continue identifying the next powers of 2: Repeat the steps to find the next powers of 2 that fit into the remaining value. For 27, the largest power of 2 is 2^4 = 16. 27 - 16 = 11. For 11, the largest power of 2 is 2^3 = 8. 11 - 8 = 3. For 3, the largest power of 2 is 2^1 = 2. 3 - 2 = 1. Finally, for 1, the largest power of 2 is 2^0 = 1. 1 - 1 = 0.

7 Step 5 -Write the binary representation: Write a 1 for each of the powers of 2 used and 0 for those that weren’t used. 1 in the 2^6 place 1 in the 2^5 place 1 in the 2^4 place 1 in the 2^3 place 0 in the 2^2 place 1 in the 2^1 place 1 in the 2^0 place Therefore, 1111011 is 123 in binary.

8 Grouping Method:In this method, we divide the number 123 by 2. Let's see the step-by-step conversion.

9 Step 1 -Divide the given number 123 by 2. 123 / 2 = 61. Here, 61 is the quotient, and 1 is the remainder.

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

11 Step 3 -Repeat the process. 30 / 2 = 15. Quotient is 15 and remainder is 0. 15 / 2 = 7. Quotient is 7 and remainder is 1. 7 / 2 = 3. Quotient is 3 and remainder is 1. 3 / 2 = 1. Quotient is 1 and remainder is 1. 1 / 2 = 0. Quotient is 0 and remainder is 1.

12 Step 4 -Write the remainders from bottom to top. Therefore, 123 (decimal) = 1111011 (binary).