71 in Binary
2026-02-28 19:07 Diff
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71 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 71 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.

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128

Since 128 is greater than 71, we stop at 2^6 = 64.

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 less than or equal to the given number, 71. 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 71. 71 - 64 = 7.

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, 7. So, the next largest power of 2 is 22, which is less than or equal to 7. Now, we have to write 1 in the 22 place. And then subtract 4 from 7. 7 - 4 = 3.

Step 4 - Continue with the next largest power of 2: Now, we find the largest power of 2 that fits into 3, which is 21. Write 1 in the 21 place and subtract 2. 3 - 2 = 1.

Step 5 - Write the final 1: The remaining number is 1, which is 20, so write 1 in the 20 place. Now, by substituting the values, we get, 1 in the 20 place 1 in the 21 place 1 in the 22 place 0 in the 23 place 0 in the 24 place 0 in the 25 place 1 in the 26 place

Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 71 in binary. Therefore, 1000111 is 71 in binary.

Grouping Method: In this method, we divide the number 71 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 71 by 2. 71 / 2 = 35. Here, 35 is the quotient and 1 is the remainder.

Step 2 - Divide the previous quotient (35) by 2. 35 / 2 = 17. Here, the quotient is 17 and the remainder is 1.

Step 3 - Repeat the previous step. 17 / 2 = 8. Now, the quotient is 8, and 1 is the remainder.

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

Step 5 - Repeat the previous step. 4 / 2 = 2. Here, the remainder is 0.

Step 6 - Repeat the previous step. 2 / 2 = 1. Here, the remainder is 0.

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, 71 (decimal) = 1000111 (binary).