The precision is fixed, which is exactly 53 binary digits for double-precision (or 52 if we exclude the implicit leading 1). This comes out to about 15 decimal digits. The OP asked me to elaborate on why having exactly 53 binary digits means “about” 15 decimal digits. To understand this intuitively, let’s consider a less-precise … Read more
Strictly speaking, the term “byte” can actually refer to a unit with other than 256 values. It’s just that that’s the almost universal size. From Wikipedia: Historically, a byte was the number of bits used to encode a single character of text in a computer and it is for this reason the basic addressable element … Read more
Two’s complement came about when someone realized that ‘going negative’ by subtracting 1 from 0 and letting the bits rollunder actually made signed arithmetic simpler because no special checks have to be done to check if the number is negative or not. Other solutions give you a discontinuity between -1 and 0. The only oddity … Read more
Consider below example Convert 2.625 to binary. We will consider the integer and fractional part separately. The integral part is easy, 2 = 10. For the fractional part: 0.625 × 2 = 1.25 1 Generate 1 and continue with the rest. 0.25 × 2 = 0.5 0 Generate 0 and continue. 0.5 × 2 = … Read more
29 = 512 values, because that’s how many combinations of zeroes and ones you can have. What those values represent however will depend on the system you are using. If it’s an unsigned integer, you will have: 000000000 = 0 (min) 000000001 = 1 … 111111110 = 510 111111111 = 511 (max) In two’s complement, … Read more
Take a look at the PNG spec. This format has some very good rationale behind it. Also, decide what’s important for your future format: compactness, compatibility, allowing to embed other formats (different compression algorithms) inside it. Another interesting example would be the Google’s protocol buffers, where size of the transferred data is the king. As … Read more
Of course. It’s more commonly called machine code. It’s basically assembly language without the mnemonic devices. Someone who knows assembly very well could program in machine code with additional effort, referring to opcode listings (e.g. x86) as needed. Would I do it? No. Even assembly is only useful in rare circumstances, and there’s no reason … Read more
In university I learned it this way: Multiply by two take decimal as the digit take the fraction as the starting point for the next step repeat until you either get to 0 or a periodic number read the number starting from the top – the first result is the first digit after the comma … Read more
What you are seeing is a marketing stunt. Since non-technical people don’t know the difference between Metric Meg, Gig, etc. against the binary Meg, Gig, etc. marketers for storage will use the Metric calculation, thus 1000 Bytes == 1 KiloByte. This can cause issues with development or highly technical people so you get the idea … Read more
The primary advantage of two’s complement over one’s complement is that two’s complement only has one value for zero. One’s complement has a “positive” zero and a “negative” zero. Next, to add numbers using one’s complement you have to first do binary addition, then add in an end-around carry value. Two’s complement has only one … Read more