Chapter 2 – Number Systems
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Octal numbers are those whose base is 8. Octal numbers have a set of only 8 digits; they are 0, 1, 2, 3, 4, 5, 6 and 7. Binary numbers are those whose base is 2. They have only 2 digits, 0 and 1. We can also refer to each digit as being turned off or on. The first digit in octal, matches the 3 digits of its binary equivalent from left to right, the next one the next 3 remaining binary digits and so on. First of all, we will draw an example grid to have at hand in order to convert from binary to decimal, assuming that the LSB Less Significant Bit is at the convert binary and hexadecimal values to octal 243 side and that we will work with byte-length binary numbers:.
In this example, we convert the binary number to decimal. To get decimal numbers from binary ones, we have to place the binary number within the lower row of this grid and sum convert binary and hexadecimal values to octal 243 the decimal numbers above digits 1. In this case, it is We keep repeating the process confidently while our sum keeps producing a result below our decimal number Convert binary and hexadecimal values to octal 243 way, we end up turning on the bit below 2 and 1, so we finally have our desired binary number:.
Now getting our octal number is the easiest part. We split our binary number into groups of 3, from right to left:. Now we just convert our splited parts back to decimal and write down each resulting digit below the corresponding binary part.
Although this is a very good practice from the binary point of view, there is a quicker method for conversion. The algorithm works as follows:. Get the decimal number for the octal We take each digit and convert it to a binary number, from right to left just to avoid making mistakes. We place the binary number making it match the right side. For these examples, we just assume that it is on the right side. Hexadecimal numbers convert binary and hexadecimal values to octal 243 in base That means that each hexadecimal digit has 16 units.
So how do we represent numbers, 10, 11, 12, 13, 14, and 15? But we will also explain hexadecimal numbers around binary numbers, so here it is basic reference table.
By using the same octal algorithm, you can also get hexadecimal numbers out of decimals without trouble:. The scientific notation was conceived to easily represent numbers that are either too large or too small. Of course you can place a zero 0 each time you move the dot to the left or to the right, making the conversion in one shot that way. Numeric Systems An overview of numeric systems. Posted on December 7, by Ernesto Garbarino. Site proudly generated by Hakyll.