67 in Binary
2026-02-28 08:33 Diff
https://brightchamps.com/en-us/math/numbers/67-in-binary

67 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 67 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 67, 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, 67. 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 67. 67 - 64 = 3.

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, 3. So, the next largest power of 2 is 21, which is less than or equal to 3 (in this case equal). Now, we have to write 1 in the 21 places. And then subtract 2 from 3. 3 - 2 = 1.

Step 4 - Identify the unused place values: In step 2 and step 3, we wrote 1 in the 2^6 and 2^1 places. Now, we can just write 0s in the remaining places, except for 20. Now, by substituting the values, we get, 1 in the 20 place 1 in the 21 place 0 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 5 - Write the values in reverse order: We now write the numbers upside down to represent 67 in binary. Therefore, 1000011 is 67 in binary.

Grouping Method: In this method, we divide the number 67 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 67 by 2. 67 / 2 = 33. Here, 33 is the quotient and 1 is the remainder.

Step 2 - Divide the previous quotient (33) by 2. 33 / 2 = 16. Here, the quotient is 16 and the remainder is 1.

Step 3 - Repeat the previous step. 16 / 2 = 8. Now, the quotient is 8, and 0 is the remainder.

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

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

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

Step 7 - Divide the quotient (1) by 2. 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, 67 (decimal) = 1000011 (binary).