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This article is about what the range of 16-bit binary numbers is. The editor thought it was very practical, so I shared it with you as a reference. Let's follow the editor and have a look.

16-bit unsigned binary numbers range from 0 to 65535 (that is, 2 to the 16th power minus 1); 16-bit signed binary numbers range from (2 to the 15th power minus 1) plus a plus or minus sign, but complements are usually used in computers. The range is "- 32768" to "32767".

The range of integers represented by 16 binary bits

If it is unsigned, it is 0 to 65535 (that is, 2 to the power of 16 minus 1)

If it is signed, then the highest bit is regarded as a symbolic bit, which ranges from (2 to the 15th power-1) plus a plus or minus sign from-32767 to + 32767, but the complement is usually used in the computer, so when signed, the range is from-32768 to 32767.

Details:

All bits of unsigned binary numbers are numeric digits, so positive or negative is not considered. 16-bit binary can represent a total of 2 ^ 16 numbers, that is, 65536 numbers, with a minimum of 0000 0000 0000 and a maximum of 1111 1111 1111, that is, zero 65535.

The first bit of a signed binary number is a sign bit, 0 is positive, 1 is negative, and all other digits are numeric bits. The following is divided into original code, inverse code, complement code to discuss:

1. In the case of the original code, the minimum 16-bit binary number is 1111 1111 1111 and the maximum is 0111 1111 1111 1111, that is,-32767 to 32767.

2. In the case of anti-code, because the inverse code is only bit-by-bit inversion of the original code, the symbol bit remains the same, so the actual representation range will not change.

3. In the case of complement, because the complement of 0 is unique, that is, 0000 0000 0000, so 1000 0000 0000 0000 means not 0, but-32768. So in the case of complement, the minimum 16-bit binary number is 1000 0000 0000 0000 and the maximum is 0111 1111 1111 1111, that is,-32768 32767.

In summary, the 16-bit unsigned binary number represents a range of 0,65535, while the 16-bit signed binary number represents a range of-32768,32767 (in the case of complement).

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