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• 5. Let be a set of five positive integers the maximum of which is at most 9. Prove that the sumsof
• 4. Identify all of the data dependencies in the following code running in a 5-stage pipelinedMIPS CP
• 【題組】(b) Apply the above exponential generating function to find the answer of the abovecounting wher
• 2. Given one logical circuit (as shown in Figure 1) and the corresponding truth table is providedin
• 【題組】1.2 Show that if A is idempotent, then is idempotent.
• 3. Let Σ= [0, 1] be an alphabet and A = [1, 00, 10] be a subset of Σ*.【題組】(a) For each integer n ≥ 1
• 5. For a system with 32-bit address, the CPU uses a 4-way set associate cache with blocksize of 16 b
• 【題組】5.2 Assume each block requires 2 extra valid bits. What is the size of the cache memory?
• 【題組】1.3 Is A+B idempotent? Justify your answer.
• 【題組】1.4Find all values of k for which kA is also idempotent.
• 6. (a) Fermat's Theorem. If is a prime, prove that for each .
• 2. A periodic signal x(t) with a period T0= 10, 0 ≤t ≤ 10 by the equation 【題組】2.1 Sketch the periodi
• 【題組】(b) For each integer n z 1, let bn be the number of strings in A* which are of length n andexact
• 6. Given the following datapath for the single-cycle implementation of a computer and thedefinition
• 13. 有一廠商承包某一展覽會場造景工程，雙方於契約內容明定下列條約：壹、簽約後在展覽會場種下造景植栽 1000 株。貳、六個月後展覽會場存活的造景植栽比率須達 95%。承包廠商根據過去種植經驗，發現
• 第 18 至 19 題為題組 某國際服飾品牌計畫在 A、B、C、D、E、F 六個城市設立門市。成立之初，準備在六個城市共設立 15 間分店，每個城市至少有兩家分店；為使各家分店之間能夠迅速調貨，要求在
• 10.If = -4x+2y and y = 1 when x =0, what is x wheny= 3?(AB)-3(AC)2 (AD)1 (AE)0 (BC)-2 (BD)3(BE) None
• 【題組】2.2 Determine the DC coefficient of the Fourier series, ao.
• 【題組】2.3 Use the Fourier analysis integral to find al, the first Fourier series coefficient.
• 3. One differential equation y" +3y'+2y= as y(0)=0 and y'(0)=1.【題組】3.1 Please solve t
• 【題組】2.4 If we add a constant valie of one to x(t), we obtain the signal y(t) = 1 + x(1) with y(t) gi
• 4. Consider the additive group (,+).【題組】(a) What is the order of 6? Why?
• 8.Let with . Prove that if and , then .
• 三、選填題 14. 在坐標平面上，若圓 Γ 完全落在四個不等式：x−y  ≤ 4、x−y≥−2、x+y ≤18、x+y≥−24所圍成的矩形區域內，則 Γ 最大可能面積為______π 。（化成最簡分數
• 【題組】3.2 Please verify your answer by using Laplace transformation.