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Unformatted text preview: 44 VLSI Test Principles and Architectures In order to control the data output q of the D flip-flop to 0, the data input d and the reset signal r can be set to 0 while applying a rising clock edge (a 0-to-1 transition) to the clock CK. Alternatively, this can be accomplished by setting r to 1 while holding CK at 0. Because a clock pulse is not applied to CK, a 1 is not added to the sequential controllability calculation in the second case; therefore, the combinational and sequential 0-controllability measures of q are: CC0 q = min CC0 d + CC0 CK + CC1 CK + CC0 r CC1 r + CC0 CK SC0 q = min SC0 d + SC0 CK + SC1 CK + SC0 r + 1 SC1 r + SC0 CK Here, CC0(q) measures how many signals in the circuit must be set to control q to 0, whereas SC0(q) measures how many flip-flops in the circuit must be clocked to set q to 0. The only way to control the data output q of the D flip-flop to 1 is to set the data input d to 1 and the reset signal r to 0 while applying a rising clock edge to the clock CK. Hence, CC1 q = CC1 d + CC0 CK + CC1 CK + CC0 r SC1 q = SC1 d + SC0 CK + SC1 CK + SC0 r + 1 Next, we calculate the combinational and sequential observability measures of all signals. The data input d can be observed at q by holding the reset signal r at 0 and applying a rising clock edge to CK. Hence, CO d = CO q + CC0 CK + CC1 CK + CC0 r SO d = SO q + SC0 CK + SC1 CK + SC0 r + 1 The asynchronous reset signal r can be observed by first setting q to 1 and then holding CK at the inactive state 0. Again, a 1 is not added to the sequential controllability calculation because a clock pulse is not applied to CK: CO r = CO q + CC1 q + CC0 CK SO r = SO q + SC1 q + SC0 CK There are two ways to indirectly observe the clock signal CK at q: (1) set q to 1, r to 0, and d to 0 and apply a rising clock edge at CK; or (2) set both q and r to 0, set d to 1, and apply a rising clock edge at CK. Hence, CO CK = CO q + CC0 CK + CC1 CK + CC0 r + min CC0 d + CC1 q CC1 d + CC0 q SO CK = SO q + SC0 CK + SC1 CK + SC0 r + min SC0 d + SC1 q SC1 d + SC0 q + 1 ...
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This note was uploaded on 05/16/2011 for the course ENGINEERIN mp108 taught by Professor Elbarki during the Spring '08 term at Alexandria University.
- Spring '08