Is something like the following code possible within a shell script?
var1=0xA (0b1010)
if ( (var1 & 0x3) == 0x2 ){
    ...perform action...
}
Just to make my intentions 100% clear my desired action would be to check bits of var1 at 0x3 (0b0011) and make sure that it equals 0x2 (0b0010)
 0b1010
&0b0011
_______
 0b0010 == 0x2 (0b0010)
                Bit manipulation is supported in POSIX arithmetic expressions:
if [ $(( var1 & 0x3 )) -eq $(( 0x2 )) ]; then
However, it's a bit simpler use an arithmetic statement in bash:
if (( (var1 & 0x3) == 0x2 )); then
                        Yes, this is entirely possible:
#!/bin/bash
var1=0xA # (0b1010)
if (( (var1 & 0x3) == 0x2 ))
then
  echo "Match"
fi
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