__52 bits__ / \ 1.00000...00000 * 2**53 Large power of two + 1.00000...00000 * 2**0 1 -------------------------- 1.00000...00000 * 2**53 + 0.00000...000001 * 2**53 Normalized exponents -------------------------- 1.00000...000001 * 2**53 But we have limited number of bits -------------------------- 1.00000...00000 * 2**53 Original large power of two