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A 32-bit register can store 2 32 different values. The range of integer values that can be stored in 32 bits depends on the integer representation used. With the two most common representations, the range is 0 through 4,294,967,295 (2 32 − 1) for representation as an binary number, and −2,147,483,648 (−2 31) through 2,147,483,647 (2 31 − 1) for representation as two's complement.
A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23) × 2 127 ≈ 3.4028235 ...
The decimal number 0.15625 10 represented in binary is 0.00101 2 (that is, 1/8 + 1/32). (Subscripts indicate the number base.) Analogous to scientific notation, where numbers are written to have a single non-zero digit to the left of the decimal point, we rewrite this number so it has a single 1 bit to the left of the "binary point". We simply ...
For the exchange of binary floating-point numbers, interchange formats of length 16 bits, 32 bits, 64 bits, and any multiple of 32 bits ≥ 128 [e] are defined. The 16-bit format is intended for the exchange or storage of small numbers (e.g., for graphics).
On a typical computer system, a double-precision (64-bit) binary floating-point number has a coefficient of 53 bits (including 1 implied bit), an exponent of 11 bits, and 1 sign bit. Since 2 10 = 1024, the complete range of the positive normal floating-point numbers in this format is from 2 −1022 ≈ 2 × 10 −308 to approximately 2 1024 ≈ ...
The number of bits needed for the precision and range desired must be chosen to store the fractional and integer parts of a number. For instance, using a 32-bit format, 16 bits may be used for the integer and 16 for the fraction. The eight's bit is followed by the four's bit, then the two's bit, then the one's bit.
Number drill bit gauge sizes range from size 80 (the smallest) to size 1 (the largest) followed by letter gauge size A (the smallest) to size Z (the largest). Although the ASME B94.11M twist drill standard, for example, lists sizes as small as size 97, sizes smaller than 80 are rarely encountered in practice.
Audio bit depth. An analog signal (in red) encoded to 4-bit PCM digital samples (in blue); the bit depth is four, so each sample's amplitude is one of 16 possible values. In digital audio using pulse-code modulation (PCM), bit depth is the number of bits of information in each sample, and it directly corresponds to the resolution of each sample.