How to Calculate 8-Bit Sequence

Binary is the foundation of computer software.

Bits are the most fundamental building blocks of computer software. A bit can be either 1 or 0, on or off. Eight bits together form a byte. Each digit of an 8-bit sequence represents a power of two, and through this, an 8-bit sequence can represent a number between 0 and 255. With the aid of a calculator, it is simple to calculate an 8-bit sequence.

Instructions

1. Write down the 8-bit sequence. For the sake of this article, we will use the example of 10110001.

2. Expand the sequence as a summation. Each of the digits represents a power of 2, with the rightmost digit representing 2^0 and the leftmost representing 2^7. Expanding our example will yield: 1*2^7+0*2^6+1*2^5+1*2^4+0*2^3+0*2^2+0*2^1+1*2^0.

3. Compute each power of two, discarding terms with zero in front. In our example, this gives: 128+32+16+1.

4. Sum up the remaining terms. In our case: 128+32+16+1 = 177.

5. Write down the final result. Concisely, our example is 10110001 = 177.

References

• "Discrete Mathematics for Computer Science"; Kenneth P. Bogart; Clifford Stein and Robert L. Drysdale; 2006