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prelim2_fa03 - ECE/CS314 Fall 2003 Prelim 2 25 November...

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ECE/CS314 Fall 2003 Prelim 2 25 November 2003 OH 155 7:30-9:00 PM Directions: Open book, notes. No laptops allowed. Answer every question in the exam booklet provided. Do not turn over this cover page until instructed to do so. Several of the questions refer to the Reference Datapath diagram, a copy of which is provided.
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1 (15 points): Floating Point Arithmetic Consider the following “half-precision” 16-bit floating point format: it uses exactly the sam format as IEEE single-precision, except that the mantissa is only 7 bits as opposed to 23. a) Give the binary representation for 1024 and 7 in half-precision floating point. Add the two numbers, showing intermediate results after each step (align, add, renormalize). You may leave the results in minary format. Assume round-to-nearest-even mode. b) Give the binary representation for 1/3 and 2/3 in half-precision floating point. Add these two numbers, again showing the intermediate results after each step (align, add, renormalize), leaving the results in binary format, and assuming round-to-nearest mode. 2 (15 points): A Recursive CAST description Consider the following CAST description. define Ckt(int L; int N)(node [N] a; node[L] b; node c) { [ L == 1 -> node _b0; Inv()(b[0], _b0); And2 A0(a[0], _b0,); And2 A1(a[1], b[0],); Or2()(A0.out, A1.out, c); ] [ L > 1 -> Ckt(L-1,N/2) CLo(a[0..N/2-1], b[0..L-2],); Ckt(L-1,N/2) CHi(a[N/2..N-1], b[0..L-2],); Ckt(1,2) ({CLo.c, CHi.c}, {b[L-1]}, c); ] } a) Give the gate diagram for the circuit produced by calling Ckt(2, 4)(...) . b) Describe in words what this circuit does (and in general what Ckt(L, N)(...) does) 3 (15 points): Caches a) For some applications it is advantageous to introduce a small (e.g. 8-entry) fully associative cache called a victim cache that stores cache lines that have receently been evicted (i.e. replaced by other data) from the memory cache. The victime cache is
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