Semi-logarithmic number systems, which are intermediate between the standard floating-point systems and logarithmic systems, are described and analyzed. They are parameterized by an integer, k, which corresponds to the number of hidden bits in their binary representations. When k = 0, a standard floating-point system is described, and when k ≥ n (the number of bits in the mantissa), a logarithmic system results. The idea is to choose a suitable value for k, between zero and n, in order to achieve an appropriate balance between fast multiplication and short lookup tables for addition. Algorithms for multiplication, division, and addition and subtraction are outlined, and an error analysis is given.