Consider a function $g(x)={|}_{{?}_{?}}lo{g}_2(1+x{)}_{{?}_{?}}|$ with the logarithm and floor

functions that may determine the transmission rate in a communication system.

$x$ being a $3-$bit unsigned integer, implement the function $g(x)$ with a smallest

number of

a$.3-$to$-8$ decoders and AND$/$OR gate$($s$).$

b$.2-$to$-4$ decoders and AND$/$OR gate$($s$).$

c$.$ priority encoders.

d$.8$x$1$ MUX's.

e$.4$x$1$ MUX's and $2$x$1$ MUX's.

f$.$ only $2x1$ MUX's.

Complements of the variables are not available. Logic levels $0$ and $1$ are

available.