Binary fractions, fixed-point representation, normalised floating-point numbers (mantissa and exponent in two's complement), conversion, rounding and underflow/overflow, and the precision/range trade-off.
Binary fractions and fixed-point
A fixed-point binary number places the binary point at a fixed position. To the right of the point the place values continue as negative powers of two: 0.5, 0.25, 0.125, … For example 0101.1010 = 4 + 1 + 0.5 + 0.125 = 5.625.
Fixed-point is simple but wastes bits and has a limited range for a given word size — you must reserve enough bits for both the largest whole number and the smallest fraction you need.
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