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Ex Design a Full $-$ Adder using two Half $-$ Adder and OR gate, draw the Block diagram and logic circuit?

Design a BCD Adder

$A=A1A0$ and $B=B1B0$ are $2-$bit binary numbers. What is the Boolean Function E that satisfies the condition $$ if $F1=A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}+A(B+C)a-A"$

Using decoder and extra gates, design the combination circuit defined $by$ the following Boolean functions: $F1=A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}+A(B+C)$

$a-$ using decoder and $OR$ gates?

$b-$ using decoder and NOR gates?

$c-$ using decoder and NAND gates?

$d-$ using $8-1$ Mux

$e-$ using $4-1$ Mux

$f-$ using $16-1$ Mux

Design $8-1$ Mux using $2$:$1$ Mux