How soon after exposure to hiv does it take for antibodies to show up in blood? is 4 months conclusive?

HIV: Generally two weeks is the time for antibody development, but measurable antibodies against HIV may, in rare cases, take as long as 6 months to develop. If one wishes to exclude those rare instances and not wait, then a pcr for viral RNA is available (but expensive) and if negative means that you do not have HIV infection.

Should be..: Most people seroconvert in 2-3 weeks but there are some later outliers.