EE 457 Quiz Solutions University of Southern California EE 457

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1 ( points) min. 1.1 A and B are negative numbers represented in 2’s complement notation. A is 16-bit in size and B is 8-bit in size. For A to be equal to B, all the 8 A bits (A[14:7]) shall be _... _______________ (all zeros / all ones) __________ (and / or) the reset of the 7 A bits (A[6:0]) shall be equal to the corresponding 7 B bits (B[6:0]) . For A to be less than B (like in -3 is less than -2), it is enough if any of the 8 A bits (A[14:7]) is a ________ (zero / one). On the other hand , if all those 8 A bits (A[14:7]) are _______________ (all zeros / all ones), then, for A to be less than B, we need the 7-bit A (A[6:0]) to be ___________ (lower / higher) than the corresponding 7-bit B (B[6:0]). Here we compare the two 7-bit numbers treating them as __________ (signed / unsigned) 7-bit numbers. 1.2 Mealy machine design: Browse through the state diagram on the next page first. Here, we perform serial inspection of bits of A (or bits of A and B) to compare them. A is a 16-bit number, but for this part of the question, B can be any where between 8-bit to 16-bit number. Here, we are allowed to inspect at a time (in a clock) one bit of A (A[I]) and (simultaneously, if needed) one bit of B (B[J]). The I and the J are indices into the A and B respectively. I is initialized to 15. J is initiated to Jini (Jinitial) which can be anywhere between 7 through 15 (corresponding to the B sizes of 8-bit to 16-bit ). You will be needing to compare I and J to see when they are equal. Note: Your TA says that ,after START is given, you should not take more than 16 clocks. After all, A is 16 bits and B is at most 16 bits. So decrement I and/or J as soon as possible! 1.2.1 Suppose B is an 8-bit number. State an example of A and B (in binary) such that the conclusion is drawn in the least number of clocks. A = _______________________________ ; B = _______________ ; How many clocks are spent in INS_AI_BJ state for the above numbers? ________ State an example of A and B (in binary) such that the conclusion is drawn in the most number of clocks. A = _______________________________ ; B = _______________ ; How many clocks are spent in INS_AI_BJ state for the above numbers? ________ 1.2.2 Since A and B are negative, there is no point looking at A[15] and B[Jini]. True / False 1.2.3 Since A’s size is fixed at 16-bit, if A is equal to B (equal in value, but not necessarily in size), it takes the same number of clocks to compare A and B, irrespective of the size of B. True / False ee457_Quiz_fl2010.fm 10/1/10 EE457 Quiz - Fall 2010 2 / 9 C Copyright 2010 Gandhi Puvvada 1.2.4 State diagram: Complete the 7 missing state transition conditions for 7 transitition arrows. Complete RTL for the three states. In state C_I_J (compare I and J), you would like to decrement _______________________________________________ (I / J / I or J / I and J / I unconditionally and J conditionally / neither I nor J). Crucial point: You want to arrive in INS_AI_BJ with the right combination of I and J whether you arrive from C_I_J or INS_AI . If B is an 8-bit number (B[7:0]), the first pair to be compared in INS_AI_BJ is ______________ (A[7],B[7] / A[6],B[6] / neither). And if B is a 16-bit number (B[15:0]), the first pair to be compared in INS_AI_BJ is __________________ (A[15],B[15] [Show More]

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