| A numeral system (or system of numeration) is a mathematical notation for representing a set of numbers by symbols in a consistent manner. It can be seen as the context that allows the numeral “11” to be interpreted as the binary numeral for three, the decimal numeral for eleven, or other numbers in different bases. |
| Ideally, a numeral system will: |
| * Represent a useful set of numbers (e.g. all whole numbers, integers, or real numbers) |
| * Give every number represented a unique representation (or at least a standard representation) |
| * Reflect the algebraic and arithmetic structure of the numbers. |
| For example, the usual decimal representation of whole numbers gives every whole number a unique representation as a finite sequence of digits, with the operations of arithmetic (addition, subtraction, multiplication and division) being present as the standard algorithms of arithmetic. |
| As a Software professional, should you care about hardware? |
| Some Software Professional look at computer hardware the same way many drivers look at their Bikes: the use of a Bike doesn’t require the knowledge of how to build one. |
| Knowing how to design and build a computer may not be vital to the computer professional, but it goes a long way toward improving their skills, i.e., making them better drivers. |
| For anyone going into a career involving computer programming, computer system design, or the installation and maintenance of computer systems, the principles of computer organization provide tools to create better designs. |
| These include: |
| • System design tools –
The same design theories used at the lowest level of system design are also applied at higher levels.For example, the same methods a circuit board designer uses to create the interface between a processor and its memory chips are used to design the addressing scheme of an IP network. |
| Software design tools –
The same procedures used to optimize digital circuits can be used for the logic portions of software. Complex blocks of if-statements, for example, can be simplified or made to run faster using these tools. |
| • Improved troubleshooting skills –
A clear understanding of the inner workings of a computer gives the technician servicing it the tools to isolate a problem quicker and with greater accuracy. |
| • Interconnectivity –
Hardware is needed to connect the real world to a computer’s inputs and outputs. Writing software to control a system such as an automotive air bag could produce catastrophic results without a clear understanding of the architecture and hardware of a microprocessor. |
| This means Software Engineer with experience in hardware design has a significant advantage over hardware engineers in this market. |