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Week04 - ULI101 Week 04 Week Overview Data Representation...

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ULI101 Week 04
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Week Overview Data Representation Binary, octal, decimal and hexadecimal numbering systems Number conversions Unix file permissions
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Data Representation Why Study Data Representation? Computers process and store information in binary format For many aspects of programming and networking, the details of data representation must be understood C Programming – sending information over networks, files Unix / Linux – setting permissions for files and directories Web Pages – setting color codes
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Data Representation In terms of this course, we will learn how a simple decimal number (integer) is stored into the computer system as a binary number. We will also learn other numbering systems (octal and hexadecimal) that can be used as a “short-cut” to represent binary numbers.
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Data Representation Before we learn numbering systems, we have to “go- back in time” to see how we learned the decimal numbering system. The decimal numbering system (base 10) uses 10 symbols for each digit (0, 1, 2, … 9). Since most humans have 10 extensions on their hands (2 thumbs, 8 fingers), many suspect that is why humans work with decimal numbers.
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Data Representation Decimal Numbers Back in grade school we learn how to understand decimal numbers. For example, take the decimal number 3572 . In grade school, we probably learned to break-down this number as follows: 3 thousands 5 hundreds 7 tens 2 ones
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Data Representation Decimal Numbers Another way to look at this number is multiplying the digit by 10 (the numbering base) raised to increasing powers (starting at 0 from the “ones” and moving towards the higher digits) 3 thousands = 3 x 10 3 = 3 x 1000 5 hundreds = 5 x 10 2 = 5 x 100 7 tens = 7 x 10 1 = 7 x 10 2 ones = 2 x 10 0 = 2 x 1 This way of understanding decimal numbers is the basis for math operations such as addition, subtraction, multiplication, decimal numbers, etc!
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Data Representation Binary Numbers We can use a similar method to convert a binary number to a decimal number. We do the same thing in the previous slide, but we multiply by base 2 instead of base 10. Take the binary number 1101: 1 x 2 3 = 1 x 8 = 8 1 x 2 2 = 1 x 4 = 4 0 x 2 1 = 0 x 2 = 0 1 x 2 0 = 1 x 1 = 1 Remember, start from the right-hand-side and move to the left. + 13 Therefore, 1101 in binary is 13 in decimal . For programmers, the 8-bit binary number 00001101 can represent the unsigned integer 13 !
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Data Representation Octal Numbers The octal numbering system (base 8) uses 8 symbols for each digit (0, 1, 2, … 7). We can use the same process in the previous slide to convert an octal number to a decimal number (but use base 8 instead!) . Convert the octal number 2741 to decimal: 2 x 8 3 = 2 x 5 1 2 = 1 0 2 4 7 x 8 2 = 7 x 6 4 = 4 4 8 4 x 8 1 = 4 x 8 = 3 2 1 x 8 0 = 1 x 1 = 1 Remember, start from the right-hand-side and move to the left.
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