Count the number of ones in an unsigned 16-bit integer

80386 Machine Code, 4 bytes

F3 0F B8 C1

which takes the integer in cx and outputs the count in ax, and is equivalent to:

popcnt ax, cx     ; F3 0F B8 C1

And here is an 11 10 byte solution not using POPCNT:

31 C0 D1 E9 10 E0 85 C9 75 F8

which is equivalent to:

xor ax, ax        ; 31 C0   Set ax to 0
shr cx, 1         ; D1 E9   Shift cx to the right by 1 (cx >> 1)
adc al, ah        ; 10 E0   al += (ah = 0) + (cf = rightmost bit before shifting)
test cx, cx       ; 85 C9   Check if cx == 0
jnz $-6           ; 75 F8   Jump up to shr cx, 1 if not

Python 2, 17 bytes

bin(s).count('1')

The bin built-in returns the integer converted to a binary string. We then count the 1 digits:

>>> s=1337
>>> bin(s)
'0b10100111001'
>>> bin(s).count('1')
6

J (5 characters)

J has no explicit types. This does the right thing for all integers.

+/@#:

• +/ the sum
• @ of
• #: the base two representation