It is a logic design questions lab.Gray code, with its unique property of single$-$bit changes between successive values, is widely used in

applications such as rotary encoders and analog$-$to$-$digital converters. Its advantage lies in minimizing

errors during transitions, making it robust for error detection and correction in telecommunications and

electronic systems. Applying Gray code in position coding ensures smooth transitions in mechanical

systems, and its use in optical encoders reduces reading errors caused by reflections. Additionally, in

Binary Coded Decimal $($BCD$),$ Gray code simplifies the conversion between binary and decimal,

making it useful in various fields.

$1-$ Discuss the relationship between the angular resolution and the number of bits. Compute the

resolution of $4-$bits gray coded disk.

$2-$ What would be the number of bits to provide a resolution of $\frac{}{512}.$

$3-$ Write the truth table of the gray code with $4$ bits.

$4-$ Deduce the truth table of the gray code decoder $($Gray bits as inputs and ordinary binary code

as outputs$).$

$5-$ Deduce the logic functions:

$,b0(g3,g2,g1,g0),b1(g3,g2,g1,g0),$ b$2($g$3,$ g$2,$g$1,$g$0),$ b$3($g$3,$ g$2,$g$1,$g$0).$

$6-$ Using K$-$map, simplify the functions b$0,...,$ b$3.$

$7-$ Realize the gray code decoder in EWB.