Most significant bit
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In computing, the most significant bit (msb, also called the high-order bit) is the bit position in a binary number having the greatest value. The msb is sometimes referred to as the left-most bit due to the convention in positional notation of writing more significant digits further to the left.
The msb can also correspond to the sign of a signed binary number in one or two's complement notation. "1" meaning negative and "0" meaning positive.
It is common to assign each bit a position number, ranging from zero to N-1, where N is the number of bits in the binary representation used. Normally, this is simply the exponent for the corresponding bit weight in base-2 (such as in 231..20). Although a few CPU manufacturers assign bit numbers the opposite way (which is not the same as different endianness), the msb unambiguously remain the most significant bit. This may be one of the reasons why the term msb is often used instead of a bit number, although the primary reason is probably that different number representations use different numbers of bits.
By extension, the most significant bits (plural) are the bits closest to, and including, the msb.
Other uses
MSB, in all capitals, can also stand for "most significant byte". The meaning is parallel to the above: it is the byte (or octet) in that position of a multi-byte number which has the greatest potential value.