How many 1-10 number can be stored in one byte?

what is the highest decimal value for one byte
one byte is equal to
1 byte = 8 bits
decimal to binary
how many integer values can be stored in a 1 byte of data?
how many numbers can be represented with 4 bits
how many bits in a byte
how many characters can you store in a byte

I have many 1-10 numbers. In C++, is it possible to store more than two in a single byte?

I believe it's possible to store at least 2: a char is from 0-255. This means we can store a number from 0-9 and one from 10-100.

a) Is it possible to store more than 2, with some kind of bit manipulation?

b) What's the fastest way to do this?

First, if memory is not an issue, avoid it. Use signed or unsigned char to store a single value.

If you want to save memory (like transmission of data array over network or save file size), you can manipulate single bits of a byte using bit operators. For example, let's get values from 0 to 15 - it fits into 4 bits. Then

// values from 0 ot 15
unsigned char v1 = 1, v2 = 15;
// pack two values into one byte
unsigned char elem = (v1 << 4) + v2; // shift v1 to left and add v2

// unpack values
v1 = elem >> 4; // shift to right
v2 = elem & 0x0F; // clear higher 4 bits

// of course, you are going to use an array of elems

Why does a byte only have 0 to 255?, through 999, which is answered in the same manner (10^3 - 1). A choice from 10 possible values requires log(10) / log(2) ~= 3.32 bits to encode. That means that the most you can store in 8 bits is two such choices. But if you have a large number of them, you can store more than two per byte in aggregate. For example, in 32 bits you can store 9 numbers from 1 to 10 (requiring 29.9 bits), which is 2.25 per byte.

There are 10 possible numbers from 1 to 10 (obvious, I know, but it must be said). A choice from 10 possible values requires log(10) / log(2) ~= 3.32 bits to encode. That means that the most you can store in 8 bits is two such choices.

But if you have a large number of them, you can store more than two per byte in aggregate. For example, in 32 bits you can store 9 numbers from 1 to 10 (requiring 29.9 bits), which is 2.25 per byte.

How many numbers can be represented in 1 byte?, different values which can be arbitrary but there are a couple of standardized encodings that make them easy to handle mathematically. Instant free online tool for byte to character conversion or vice versa. The byte [B] to character conversion table and conversion steps are also listed. Also, explore tools to convert byte or character to other data storage units or learn more about data storage conversions.

Binary Word, What is the highest number you can get to using 1 byte? It depends if the bytes are sequential or discrete. Treating it as a straight binary 16 bit number, the highest number will be 2^16=65,536. Looking at each byte as a maximum value, it would be 256 each. If the second byte is used as the higher place values, then it’s the same as before; 65,536 counts.

How many bits are required to represent 11 values?, Analogously the binary number 1010 means: where is 10 in binary = 2 in decimal. A byte encoded this way can represent any value in the range 0… 255, and addition, subtraction, multiplication and division works pretty much the same as in the decimal system as long as we stay in the range. Can anyone Please let me know number(1) occupies how many bytes?.Between 1 and 3 bytes. I tested this (on 10.2.03): BROST@ORCL01 > create table numtest (id number(1)); Table created.

Bits and Bytes, One byte = collection of 8 bits; e.g. 0 1 0 1 1 0 1 0; One byte can store one character, How many different patterns can be made with 1, 2, or 3 bits? In general: add 1 bit, double the number of patterns; 1 bit - 2 patterns; 2 bits - 4; 3 bits - 8  So, computer memory chips are simply many, many (electronic) switches, each with the ability to represent either 0 or 1. The standard unit of measurement for storage capacity on a computer is the byte. One byte is used to represent and store one character, which can be a letter, number, or other symbol. (Or, in the case of graphics, one byte

Bits and Bytes, The largest number you can represent with 8 bits is 11111111, or 255 in decimal notation. If you have an eight bit buss, you can send bytes one after another, and the processor can A computer wouldn't be much use if it couldn't store data​. 256 combinations.Byte contains the 8 Bits and bit contains either the value 0 or 1.i.e. (2 raise to power 8 minus 1).The maximum number of value represented with a byte is 8 bits is 255 but 0 should also be considered as well as 1,

Comments
  • In principle yes since the smallest power of 2 bigger than 10 is 16 which is 2^4 and since a char is 8 bits you could store two single digits but why do you want to do this?
  • @Luka why do you think you need to save memory?
  • Not sure if I understand the question like musefan commented you can do this if you do byte conversion yourself. For example if you have two number 4 and 10, then you can store as 0x4A, two numbers in a byte. More context might help.
  • When you say "avoid it", is there a huge performance penalty, or a very small one?
  • It depends on your needs. If you need a fast access (many computations with the numbers), then avoid it. If you need small memory (data packets, file storage), then these IO operations are slow, and it's worth to perform the compression.
  • @Luka the main reason to avoid it if you don't have memory constraints is that it needlessly complicates your code.
  • great point. so, if I have one 8 byte variable = 64 bits, how many can I store?
  • Also, in that sense, I can create a huge array of chars and store tons of them, right?
  • You can store 19 digits.
  • @Luka floor( 64 * log(2) / log(10) ) = 19
  • @Luka (Not coincidentally, 2^64 is a 20-digit number. But only 19 of those are useful, because the 10^19 place can only be 0 or 1).
  • re your last line I note that since the numbers are 1-10 you need to encode 10 as 0 in this storage method. Worth being explicit I figure.