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→Week 4 - Class I
* Binary Representation of Data
** Integers
*** Integers are the basic building block of binary numbers.
*** In an unsigned integer, the bits are numbered from right to left starting at 0, and the value of each bit is <code>2<sup>bit</sup></code>. The value represented is the sum of each bit multiplied by its corresponding bit value. The range of an unsigned integer is <code>0:2<sup>bits</sup>-1</code> where bits is the number of bits in the unsigned integer.
*** Signed integers are generally stored in twos-compliment format, where the highest bit is used as a sign bit. If that bit is set, the value represented is <code>-(!value)-1</code> where ! is the NOT operation (each bit gets flipped from 0→1 and 1→2)
** Fixed-point
*** A fixed-point value is encoded the same as an integer, except that some of the bits are fractional -- they're considered to be to the right of the "binary point" (binary version of "decimal point" - or more generically, the ''radix point''). For example, binary 000001.00 is decimal 1.0, and 000001.11 is decimal 1.75.
*** An alternative to fixed-point values is integer values in a smaller unit of measurement. For example, some accounting software may use integer values representing cents. For input and display purposes, dollar and cent values are converted to/from cent values.
** Floating-point
*** Floating point numbers have three parts: a ''sign bit'' (0 for positive, 1 for negative), a ''mantissa'' or ''significand'', and an ''exponent''. The value is interpreted as <code>''sign'' mantissa * 2<sup>exponent</sup></code>.
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