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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. In a hexadecimal system, there are 16 digits, 0 through 9 followed, by convention, with A through F. That is, a hexadecimal "10" is the same as a decimal "16" and a hexadecimal "20" is the same as a decimal "32".
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
Some languages (such as COBOL and PL/I) directly support fixed-point zoned decimal values, assigning an implicit decimal point at some location between the decimal digits of a number. For example, given a six-byte signed zoned decimal value with an implied decimal point to the right of the fourth digit, the hex bytes F1 F2 F7 F9 F5 C0 represent ...
Another common way of expressing the base is writing it as a decimal subscript after the number that is being represented (this notation is used in this article). 1111011 2 implies that the number 1111011 is a base-2 number, equal to 123 10 (a decimal notation representation), 173 8 and 7B 16 (hexadecimal).
This is because the radix of the hexadecimal system (16) is a power of the radix of the binary system (2). More specifically, 16 = 2 4, so it takes four digits of binary to represent one digit of hexadecimal, as shown in the adjacent table. To convert a hexadecimal number into its binary equivalent, simply substitute the corresponding binary ...
This table illustrates an example of an 8 bit signed decimal value using the two's complement method. The MSb most significant bit has a negative weight in signed integers, in this case -2 7 = -128. The other bits have positive weights. The lsb (least significant bit) has weight 2 0 =1. The signed value is in this case -128+2 = -126.
In a move or convert operation, zero extension refers to setting the high bits of the destination to zero, rather than setting them to a copy of the most significant bit of the source. If the source of the operation is an unsigned number, then zero extension is usually the correct way to move it to a larger field while preserving its numeric ...
Ones' complement allowed for somewhat simpler hardware designs, as there was no need to convert values when passed to and from the math unit. But it also shared an undesirable characteristic with sign–magnitude: the ability to represent negative zero (−0). Negative zero behaves exactly like positive zero: when used as an operand in any ...