logicode, 610 bytes

Result [link]

AC

Code [DL]

circ xor(a,b)->(!(a&b))&(a|b)
circ nz(a)->cond a->1/0
circ eq(a,b)->!(nz(xor(a,b)))
circ add3ge5(a)->[
	var b4=(a<)|((a><)&nz(a>>))
	var b3=eq(a,1001)
	var b2=eq(a,0111)|eq(a,1000)
	var b1=!((~a)<)
	cond b4->b4+b3+b2+b1/a
]
circ car4(a)->(a<)+(a><)+(a>><)+(a>>><)
circ add3ge5l(a)->cond eq(1+a,1)->0/0+add3ge5l(~((~a)>>>>))>+add3ge5(~(car4(~a)))
circ trim4(a)->cond nz(car4(a))->a/a>>>>
circ main(o,i)->[
	var o2=add3ge5l(o)>
	cond o2<->var o2=000+o2+i</var o2=o2>+i<
	cond eq(1+i>,1)->o2/main(o2,i>)
]
circ decp(a)->@(11+a)
circ dec(a)->cond eq(1+a,1)->0/0+decp(car4(a))+dec(a>>>>)>
out dec(main(0000,binp))>

stdin

0100001101001110001111110110011111110101111101000100010111111100111001100110111010101101010100011000

stdout

333281460780575815136472388888

stderr

strace