Tugas 11 [Namira] : Computer Arithmetic

 Computer Arithmetic

Arithmetic and logic unit
-Does the calculations
-Everything else in the computer is there to  service this unit
-Handles integers
-May handle floating point (real) numbers -May be separate FPU (maths co-processor)
-May be on chip separate FPU (486DX +)

Integer Representation
-Only have 0 & 1 to represent everything -Positive numbers stored in binary
-e.g. 41=00101001
-No minus sign
-No period
-sign-Magnitude
-Two’s compliment

Sign Magnitude
Left most bit is sign bit
-0 means positive
-1 means negative
+18 = 00010010
-18 = 10010010 Problems
-Need to consider both sign and magnitude in  arithmetic
-Two representations of zero (+0 and -0)

Conversion Between Length
-Positive number pack with leading zeros -+18 = 00010010
+18 = 00000000 00010010
Negative numbers pack with leading ones -18 = 10010010
-18 = 11111111 10010010
-i.e. pack with MSB (sign bit)

Normalization
-FP numbers are usually normalized i.e. exponent is adjusted so that leading bit  (MSB) of mantissa is 1
-Since it is always 1 there is no need to store it
-(c.f. Scientific notation where numbers are  normalized to give a single digit before the  decimal point e.g. 3.123 x 103)

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