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# L7 ALU - Computer Science 230H ALU Computer Arithmetic...

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Computer Science 230H ALU – Computer Arithmetic Prepared by Michael Jack Fall 2007 Slides set 3

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ALU 2 References The information and figures for the following slides were prepared from the following source: Patterson, D., and Hennessy J., Computer Organization and Design, 3rd edition, 2005 Stallings, W., Computer Organization and Architecture: Designing for Performance 7 th edition, 2006 Hircock B., Computer Science 230 Course Notes
ALU 3 Fixed-point notation (e.g. twos complement) allows representation of a range of positive and negative integers centered on 0. The limitation of this scheme is the inability to represent very large numbers or very small fractions. Need the ability to dynamically move the decimal point to a convenient location. Floating-Point Representation

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ALU 4 FP without a Biased Exponent Format: ± S R ± E S = significand, R = radix, E = exponent. Significands are stored in a normalized format - 0.1bbb…b No need to explicitly store 1 in the data word - insert it for calculations only. Base is implicit Typically, it is assumed that the radix point is to the right of the leftmost bit (msb) of the significand, i.e. there is 1 bit to the left of the radix point. Exponents can be positive or negative values Can use biasing (excess coding) to avoid operating on negative exponents where bias is added to all exponents.
ALU 5 The leftmost bit stores the sign (0 = positive, 1 = negative) The next 8 bits store the exponent. A fixed value (bias) is subtracted from the field to get the true exponent value. Typically the bias equals (2 k-1 – 1), where K is the number of bits in the binary exponent.

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L7 ALU - Computer Science 230H ALU Computer Arithmetic...

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