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A four-bit Gray cyclic code A, where A = A3A2A¡Ao with Ao as the least significant digit, is used to represent ten angular positions of a wheel, the cyclic code being as follows: Input Code A A3 A2 Aj Ao Position 1 1 1 1 3 1 1 1 4 1 1 5 1 1 6 1 1 1 1 1 8 1 1 9 1 The remaining six possible combinations of A3A2A1A0 never occur. A recoding circuit accepts this cyclic code and gives an output code that is equal to the decimal position number but in natural binary coding. (a) Identifying the output code as B = B3B2B¡Bo in your answer, where Bo is the least significant digit, compile a truth table that completely specifies the required recoding circuit. (b) Derive the sum-of-minterms the Boolean expressions for the required outputs.
Transcribed Image Text:A four-bit Gray cyclic code A, where A = A3A2A¡Ao with Ao as the least significant digit, is used to represent ten angular positions of a wheel, the cyclic code being as follows: Input Code A A3 A2 Aj Ao Position 1 1 1 1 3 1 1 1 4 1 1 5 1 1 6 1 1 1 1 1 8 1 1 9 1 The remaining six possible combinations of A3A2A1A0 never occur. A recoding circuit accepts this cyclic code and gives an output code that is equal to the decimal position number but in natural binary coding. (a) Identifying the output code as B = B3B2B¡Bo in your answer, where Bo is the least significant digit, compile a truth table that completely specifies the required recoding circuit. (b) Derive the sum-of-minterms the Boolean expressions for the required outputs.
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