Novices sometimes ask how to get a convert an integer to a list of bits, often for the purpose of iterating over the bits somehow. Common Lisp has a rich set of functions for directly accessing the bits of an integer, so constructing an intermediate list of bits is rarely necessary.

Here are a few examples of accessing the bits of an integer.

With integer-length and logbitp to test the bit at a particular index:

(defun list-of-bits (integer)
(loop for index below (integer-length integer)
collect (if (logbitp index integer) 1 0)))

With ash to shift the integer to the right and logand to test the least-significant bit:

(defun list-of-bits (integer)
(loop repeat (integer-length integer)
for i = integer then (ash i -1)
collect (logand i 1)))

With ash to shift a one-bit mask to the left and logtest to test the mask bit against the integer:

(defun list-of-bits (integer)
(loop repeat (integer-length integer)
for mask = 1 then (ash mask 1)
collect (if (logtest mask integer) 1 0)))

With byte to construct a byte specifier and ldb to extract a field from the integer:

(defun list-of-bits (integer)
(loop for position below (integer-length integer)
collect (ldb (byte 1 position) integer)))

**update** Unfortunately, all these examples are buggy - they collect bits in the wrong order. I used loop/collect to avoid having to reverse the results, but didn’t think it through properly. Here are some updated definitions with dotimes that give the results in the intended order:

(defun list-of-bits (integer)
(let ((bits '()))
(dotimes (index (integer-length integer) bits)
(push (if (logbitp index integer) 1 0) bits))))

(defun list-of-bits (integer)
(let ((i integer)
(bits '()))
(dotimes (j (integer-length integer) bits)
(push (logand i 1) bits)
(setf i (ash i -1)))))

(defun list-of-bits (integer)
(let ((mask 1)
(bits '()))
(dotimes (i (integer-length integer) bits)
(push (if (logtest mask integer) 1 0) bits)
(setf mask (ash mask 1)))))

(defun list-of-bits (integer)
(let ((bits '()))
(dotimes (position (integer-length integer) bits)
(push (ldb (byte 1 position) integer) bits))))