Representation of Floating-Point Numbers

Final note before seeing examples: the significand contains the fraction part of a number (i.e., all the digits to the right of the binary point (.). For instance, a significand of $10001$ represents the binary fraction $0.10001$. The exponent will then magnify or diminish this number.

Example: The number represented by

+---+   +---+---+---+---+---+   +---+---+---+---+---+
| 0 |   | 1 | 0 | 1 | 0 | 1 |   | 1 | 0 | 0 | 1 | 0 |
+---+   +---+---+---+---+---+   +---+---+---+---+---+

can be understood as follows: (1) the number is positive since the sign bit is $0$. (2) to figure out what the exponent is, $10101$, subtract $15_{10}$ (the bias) from it. $10101$ in binary is $21_{10}$, so $21 - 15$ is $6$, so the exponent is $6$. (3) the significand is $10010$, which is $0.10010$ binary. Together, we get: $0.10010 \times 2^6 = 100100.0$, which is $36_{10}$.