First implementation:

name: cw
init: q0
accept: qAccept

// any strings starting with 0 will always never terminate
q0,0
q0,0,<

q0,_
q0,_,<

// strings starting with 1 may accept in certain situations
q0,1
q1,1,>

// keep reading 1s
q1,1
q1,1,>

// eventually read a 0
q1,0
q2,0,>

// then accept if there is another 1
// q2,1
// qAccept,1,>

// or reject
q2,1
qReject,1,>

New implementation:

name: cw
init: q0
accept: qAccept

// always accept any first digit
q0,0
q1,0,>
q0,1
q1,1,>

// then repeat 1s
q1,1
q1,1,>

// then check if we have a 0
q1,0
q2,0,>

// go back if it's another 0
q2,0
q1,0,<

// otherwise accept and reject
q2,1
qAccept,1,>