1 0 1 1 1 1

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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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