103 in Binary
2026-02-28 12:50 Diff
https://brightchamps.com/en-us/math/numbers/103-in-binary

103 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.

Expansion Method: Let us see the step-by-step process of converting 103 using the expansion method.

Step 1 - Figure out the place values: In the binary system, each place value is a power 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 2^5 = 32 2^6 = 64 Since 64 is less than 103, we stop at 2^6 = 64.

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 less than or equal to the given number, 103. Since 2^6 is the largest number we are looking for, write 1 in the 2^6 place. Now the value of 2^6, which is 64, is subtracted from 103. 103 - 64 = 39.

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, 39. So, the next largest power of 2 is 2^5, which is 32. Now, we have to write 1 in the 2^5 place. And then subtract 32 from 39. 39 - 32 = 7.

Step 4 - Continue the process: Next, identify the largest power of 2 that fits into 7, which is 2^2 = 4. Write 1 in the 2^2 place. Subtract 4 from 7. 7 - 4 = 3.

Step 5 - Continue with the remaining numbers: Identify the largest power of 2 that fits into 3, which is 2^1 = 2. Write 1 in the 2^1 place. Subtract 2 from 3. 3 - 2 = 1. Finally, write 1 in the 2^0 place. Subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.

Step 6 - Write the unused place values: In steps above, we wrote 1 in the 2^6, 2^5, 2^2, 2^1, and 2^0 places. Now, we can just write 0s in the remaining places, which are 2^4 and 2^3. Now, by substituting the values, we get, 0 in the 2^4 place 0 in the 2^3 place 1 in the 2^2 place 1 in the 2^1 place 1 in the 2^0 place 1 in the 2^5 place 1 in the 2^6 place So, 1100111 is 103 in binary.

Grouping Method: In this method, we divide the number 103 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 103 by 2. 103 / 2 = 51. Here, 51 is the quotient and 1 is the remainder.

Step 2 - Divide the previous quotient (51) by 2. 51 / 2 = 25. Here, the quotient is 25 and the remainder is 1.

Step 3 - Repeat the previous step. 25 / 2 = 12. Now, the quotient is 12 and the remainder is 1.

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

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

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

Step 7 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the division here because the quotient is 0.

Step 8 - Write down the remainders from bottom to top. Therefore, 103 (decimal) = 1100111 (binary).