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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

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Q: What is the 8-bit binary equivalent of a given decimal number?
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Related questions

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

It can be any decimal number between 0 and 255.


Which decimal number is correct for given binary number 11011010?

218


What is the same thing as 10101010?

The binary number 10101010 is equivalent, in decimal representation, to 128 + 32 + 8 + 2 = 170. But this answer assumes that the given number is binary - an assumption for which there is no real justification. Besides, the relationship is an equivalence, which is not quite "the same thing".


What would 011110 equal in normal math?

I assume that you are asking how to convert the binary: 011110 to decimal. First off there are 6 places in this binary number--actually five, being that the last number is 0 (a place-holder). So, charting or making a table: Binary CalculationDecimal EquivalentOriginal Binary NumberAdd together2010021212224142381824161162532002664Not givenNot given Add together the last column of numbers together will give you the decimal equivalent to the binary number: 011110.


What is the decimal number for 000011?

We don't know what the base of the given number is. Since the only digits shown are 1's, the base could be anything from 2 and up. Whatever the base is, the given number is (base + 1). If " 0 0 0 0 1 1 " is a binary number (base 2), then the decimal equivalent is 3 .


How do you find a decimal equivalent to a given number?

Take the number and divide it by 100.


Can 0.9 equivalent to the given decimal?

Yes, it can but it all depends on what the given decimal is!


Which of the decimal numbers corresponds to the binary number 00000111?

As per the 8421 rule the given binary number can be solved as : 0 0 0 0 0 1 1 1 0 0 0 0 0 4 2 1 i.e : 4+2+1 = 7 So the answer is 07 in decimal for 00000111 in binary


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How do you create an equivalent represantation for a decimal when given the percent?

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How can you find equivalent fractions to a given decimal?

You turn the decimal into a fraction. Then you can find the equivalent fraction.