What is the relationship between the binary, octal, and hexadecimal number systems? | Yahoo Answers
Nov 30, Let's explore few different number systems that are in use today and see how with simple three rules, we can build any number system we want. We can also see a special relationship between three of these number systems. Binary, octal, and hexadecimal all have bases that are powers of 2. All the other answers are correct, but I thought I would add that binary is to octal as base 10 is to base 10^3 = , and binary is to.
For example, even though bit processors may address memory sixty-four bits at a time, they may still split that memory into eight-bit pieces. This is called byte-addressable memory.
Difference between decimal and binary numbers
Historically, many CPUs read data in some multiple of eight bits. A nibble sometimes nybbleis a number composed of four bits. A person may need several nibbles for one bite from something; similarly, a nybble is a part of a byte. Because four bits allow for sixteen values, a nibble is sometimes known as a hexadecimal digit.
Base64 Octal and hex are convenient ways to represent binary numbers, as used by computers. Computer engineers often need to write out binary quantities, but in practice writing out a binary number such as is tedious and prone to errors.
Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base, "hexadecimal" or "hex", number format. In the decimal system, there are 10 digits, 0 through 9, which combine to form numbers.
In an octal system, there are only 8 digits, 0 through 7. That is, the value of an octal "10" is the same as a decimal "8", an octal "20" is a decimal "16", and so on.
Numeral Systems - Binary, Octal, Decimal, Hex
In a hexadecimal system, there are 16 digits, 0 through 9 followed, by convention, with A through F. Hexadecimal base 16 is currently the most popular choice for representing digital circuit numbers in a form that is more compact than binary. Hexadecimal numbers are sometimes represented by preceding the value with '0x', as in 0x1B Hexadecimal is sometimes abbreviated as hex. All four number systems are equally capable of representing any number. Furthermore, a number can be perfectly converted between the various number systems without any loss of numeric value.
Converting Between Binary, Octal, Decimal, and Hexadecimal Number Systems - Robot Room
At first blush, it seems like using any number system other than human-centric decimal is complicated and unnecessary. However, since the job of electrical and software engineers is to work with digital circuits, engineers require number systems that can best transfer information between the human world and the digital circuit world. It turns out that the way in which a number is represented can make it easier for the engineer to perceive the meaning of the number as it applies to a digital circuit.
In other words, the appropriate number system can actually make things less complicated. Fundamental Information Element of Digital Circuits Almost all modern digital circuits are based on two-state switches. The switches are either on or off. Because the fundamental information element of digital circuits has two states, it is most naturally represented by a number system where each individual digit has two states: For example, switches that are 'on' are represented by '1' and switches that are 'off' are represented by '0'.
It is easy to instantly comprehend the values of 8 switches represented in binary as