1143 in Binary
2026-02-28 10:51 Diff
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1143 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 1143 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 2^7 = 128 2^8 = 256 2^9 = 512 2^10= 1024 Since 2048 is greater than 1143, we stop at 2^10 = 1024.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^10 = 1024. 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, 1143. Since 2^10 is the number we are looking for, write 1 in the 2^10 place. Now the value of 2^10, which is 1024, is subtracted from 1143. 1143 - 1024 = 119.

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 2^6, which is less than or equal to 119. Now, we have to write 1 in the 2^6 places. And then subtract 64 from 119. 119 - 64 = 55.

Step 4 - Continue identifying the next largest powers: We continue this process, identifying the next largest power of 2 that fits into the result from the previous step until the remainder is 0. 55 - 32 = 23 (write 1 in the 2^5 place) 23 - 16 = 7 (write 1 in the 2^4 place) 7 - 4 = 3 (write 1 in the 2^2 place) 3 - 2 = 1 (write 1 in the 2^1 place) 1 - 1 = 0 (write 1 in the 2^0 place)

Step 5 - Identify the unused place values: In the steps above, we wrote 1s in the 2^10, 2^6, 2^5, 2^4, 2^2, 2^1, and 2^0 places. Now, we can just write 0s in the remaining places, which are 2^9, 2^8, 2^7, and 2^3. Now, by substituting the values, we get, 0 in the 2^9 place 0 in the 2^8 place 0 in the 2^7 place 1 in the 2^6 place 1 in the 2^5 place 1 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

Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 1143 in binary. Therefore, 10001110111 is 1143 in binary.

Grouping Method: In this method, we divide the number 1143 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 1143 by 2. 1143 / 2 = 571. Here, 571 is the quotient and 1 is the remainder.

Step 2 - Divide the previous quotient (571) by 2. 571 / 2 = 285. Here, the quotient is 285 and the remainder is 1.

Step 3 - Repeat the previous step. 285 / 2 = 142. Now, the quotient is 142, and 1 is the remainder.

Step 4 - Repeat the previous step. 142 / 2 = 71. Here, the quotient is 71 and the remainder is 0.

Step 5 - Repeat the previous step. 71 / 2 = 35. Here, the quotient is 35 and the remainder is 1.

Step 6 - Repeat the previous step. 35 / 2 = 17. Here, the quotient is 17 and the remainder is 1.

Step 7 - Repeat the previous step. 17 / 2 = 8. Here, the quotient is 8 and the remainder is 1.

Step 8 - Repeat the previous step. 8 / 2 = 4. Here, the quotient is 4 and the remainder is 0.

Step 9 - Repeat the previous step. 4 / 2 = 2. Here, the quotient is 2 and the remainder is 0.

Step 10 - Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1 and the remainder is 0.

Step 11 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the division here because the quotient is 0.

Step 12 - Write down the remainders from bottom to top. Therefore, 1143 (decimal) = 10001110111 (binary).