What is 167 in decimal expressed in binary?

Answer 1

To express a number in binary, first we find the greatest power of 2 which is less than or equal to the value. The first powers of 2 are:

1, 2, 4, 8, 16, 32, 64, 128, 256, ...

The highest value we will use here is 128 (the 7th power of 2). So far we have:

10000000 (binary) = 128.

Next we need to subtract 128 from 167 to find the remaining value. 167 - 128 = 39. The next value we should use is 32 because it is the largest value still less than or equal to 39. Now we have:

10100000 (binary) = 128 + 32 = 160.

39 - 32 = 7, so now we choose a 4.

10100100 (binary) = 128 + 32 + 4 = 164.

Now a 2 and a 1 will finish the process.

10100111 (binary) = 128 + 32 + 4 + 2 + 1 = 167.