Unsigned: 216-1. Signed: 215-1.
The answer depends on the number of binary digits (BITS) in the word. The largest 8-BIT hexadecimal word will be 16^8 -1 = 4,294,967,295.Nowadays, 32 and 64 bit words are common: a 64 bit word could hold a number greater than 1.1*10^77 while a 128 bit word (not yet in common use) would exceed 1.3*10^154 or a Googol^1.5
16 and 32 have a GCF of 16 because 16 is the largest positive integer that divides evenly into both of those numbers with no remainder.
16 is a composite number because it has at least one positive factor other than one or itself.
For a digital photo, bit depth is the number of colors that can be shown in the image. Because the bits can only indicate one of 2 possible states (0 or 1), the number of colors can only be powers of 2. Some examples of bit depths (and the calculation of the decimal number for those of you who know exponents) for image files are: 2-bit (2^2 = 4 colors), 4-bit (2^4=16 colors), 8-bit (2^8=256 colors), 16-bit (2^16=65,536 colors), and 24-bit (2^24=16,777,216 colors).
Unsigned: 216-1. Signed: 215-1.
65,535
216-1 or (2^16)-1
The number of data lines required in a 16-bit microprocessor is 16, in the internal view, but could be something else, such as 8, in the external view. In the 8086/8088, the processor is 16 bits, and its internal data bus is 16 bits. The 8086 provides 16 bits on the external bus, but the 8088 provides 8 bits, even though they are the same internal processor - the 8088 simply uses two memory cycles to move one word. The largest number that can be represented on a 16 bit bus depends on the interpretation of that number. An unsigned 16 bit number ranges from 0 to 65535, so 65535 is the largest value when unsigned. A 16 bit two's complement signed number ranges from -32768 to +32767, so +32767 is the largest value when signed.
That would be 216 - 1, or 65535.
In a 16 bit number there must be from zero to 16 '1'. If a bit does not have value zero then it has a value of 1. Nothing else can be represented by a bit. Example 0000 is a 4 bit number. Each bit is a zero. 1010 is also a four bit number. 0000111100001111 is a 16 bit number. 1100110011000001 is also a 16 bit number.
The most significant bit (MSB) of a 16-bit number is the leftmost bit, which carries the highest weight. In a 16-bit number, the MSB has a weight of 2^15, which is equivalent to 32,768.
Any number that is a multiple of 16 can be divided by 16 without a remainder. This means that any number that is evenly divisible by 16, such as 16, 32, 48, 64, and so on, can be divided by 16. In mathematical terms, a number n can be divided by 16 if n is equal to 16 multiplied by an integer k, where k is any whole number.
216 -1
There are 8 bits in a byte, so a two byte integer would be 16 bits. The largest 16 bit integer possible would be 11111111111111112, which is 65535 in base 10.
16
(2 to the power of 16 ) - 1 = 65535