What is the 8-bit binary equivalent of a given decimal number?

Answer 1

An eight-bit binary equivalent to a given decimal number is a number that is expressed in base two arithmetic rather than base ten. Because we're only dealing with eight bits though, the largest decimal value that we can represent is 255, which would be expressed as 11111111.

To express a number, you will place a 1 in the position for a number of values (powers of 2) that add up to the decimal number. The right-most digit is 20 (1) followed by columns (moving left) for 2, 4, 8, 16, 32, 64, and 128.

For example 00000011 would be 3, which is the sum of 21 and 20, 2+1.

Writing a Binary Equivalent (Left to Right)

To find the binary equivalent to a decimal number, there is an easy trick:

take any number, let's go with 237, and find the largest power of two that is less than that number. In the case of 237, that largest power of two below it would be 128, or 27.

237 - 128 = 109

Because we could make that subtraction, we'll write down the number 1:

1

Now we take that power of two we subtracted, and divide it by two:

128 / 2 = 64

And check to see if we can subtract from the result of our previous subtraction, 109. In this case we can, as 64 < 109, so we can do the subtraction:

109 - 64 = 45

And write down another number 1:

11

We repeat this process, this time with the number 32. Again it's smaller than our tally, 45, so we again subtract it, and add 1 to our number:

45 - 32 = 13

and our number becomes:

111

our next power of two is 16, but we can't subtract that from our tally - 13 - as that would give us a negative number. Instead, we'll not subtract it, and add a zero to our number:

1110

then we have 8, which is indeed smaller than 13, so we get:

13 - 8 = 5

11101

And again with 4:

5 - 4 = 1

111011

Two is another case where we can't subtract it, as it's bigger than our tally:

1110110

And finally, we have our final number, 1, which we can indeed subtract from our tally, giving us the final number:

11101101