using Printf

xor{T<:Bool}(a::T, b::T) = (a&~b)|(~a&b)

halfadder{T<:Bool}(a::T, b::T) = (xor(a,b), a&b)

function fulladder{T<:Bool}(a::T, b::T, c::T=false)
    (s, ca) = halfadder(c, a)
    (s, cb) = halfadder(s, b)
    (s, ca|cb)
end

function adder(a::BitArray{1}, b::BitArray{1}, c0::Bool=false)
    len = length(a)
    length(b) == len || error("Addend width mismatch.")
    c = c0
    s = falses(len)
    for i in 1:len
        (s[i], c) = fulladder(a[i], b[i], c)
    end
    (s, c)
end

function adder{T<:Integer}(m::T, n::T, wid::T=4, c0::Bool=false)
    a = bitpack(digits(m, 2, wid))[1:wid]
    b = bitpack(digits(n, 2, wid))[1:wid]
    adder(a, b, c0)
end

Base.bits(n::BitArray{1}) = join(reverse(int(n)), "")