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In binary the largest number (using IEEE binary16) representable would be: 0111 1111 1111 1111 (grouping the bits in nybbles* for easier reading). This is split as |0|111 11|11 1111 1111| which represents:

0 = sign

111 11 = exponent

11 1111 1111 = mantissa.

Using IEEE style, the exponent is offset by 011 11, making the maximum exponent 100 00

This is scientific notation using binary instead of decimal. As such there must be a non-zero digit before the binary point, but in binary this can only ever be a 1, so to save storage it is not stored and the mantissa effectively has an extra bit, which for the 10 bits specified makes it 11 bits long. Thus the mantissa represents: 1.11 1111 1111

This gives the largest number as:

1.1111 1111 11 × 10^10000

(all digits are binary, not decimal.) This expands to 1 1111 1111 1100 0000 (binary) = 0x1ffc0 = 131,008

Note that this is NOT accurate in storage - there are 6 bits which are forced to be zero, making the number only accurate to ±32 (decimal): the second largest possible real would be 1 1111 1111 1000 000 = 0x1ff80 = 130,944 - the numbers are only accurate to about 4 decimal digits; the largest decimal real number would be 1.310 × 10^5, and the next 1.309 × 10^5 and so on.

However, with proper IEEE, an exponent with all bits set is used to identify special numbers, which makes the largest possible 0111 1101 1111 1111 which is 1.1111 1111 11 × 10^1111 = 1111 1111 1110 0000 = 0xffe0 = 65504 accurate to ±16, ie the largest is about 6.55 × 10^4.

* a nybble is half a byte which is directly representable as a single hexadecimal digit.

Q: What is the Largest real number that can be stored in binary using 16 bits Where 1 bit is used for the sign 5 bits for the characteristics and 10 for the Mantissa?

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Think of the floating-point number as a number in scientific notation, for example, 5.3 x 106 (i.e., 5.3 millions). In this example, 5.3 is the mantissa, whereas 6 is the exponent. The situation is slightly more complicated, in that floating-point numbers used in computers are stored internally in binary. Some precision can be lost when converting between decimal and binary.Think of the floating-point number as a number in scientific notation, for example, 5.3 x 106 (i.e., 5.3 millions). In this example, 5.3 is the mantissa, whereas 6 is the exponent. The situation is slightly more complicated, in that floating-point numbers used in computers are stored internally in binary. Some precision can be lost when converting between decimal and binary.Think of the floating-point number as a number in scientific notation, for example, 5.3 x 106 (i.e., 5.3 millions). In this example, 5.3 is the mantissa, whereas 6 is the exponent. The situation is slightly more complicated, in that floating-point numbers used in computers are stored internally in binary. Some precision can be lost when converting between decimal and binary.Think of the floating-point number as a number in scientific notation, for example, 5.3 x 106 (i.e., 5.3 millions). In this example, 5.3 is the mantissa, whereas 6 is the exponent. The situation is slightly more complicated, in that floating-point numbers used in computers are stored internally in binary. Some precision can be lost when converting between decimal and binary.

A nibble is 4 bits, so the largest unsigned number is 1111, or 15. Also, the largest signed number is 0111, or 7.

A 32 binary number is a number stored by a computer in 32 bits. it can represent: 1) An unsigned number in the range 0 to 4,294,967,295 2) A signed number in the range -2,147,483,648 to 2,147,483,647 3) A single precision IEEE floating point number with 1 sign bit, 8 exponent bits and 23 mantissa bits give an accuracy of about 7.2 decimal digits and a range of ± 10^-38 to 10^38

The number 4693 in binary is 1001001010101

No, binary is a number system.A binary digit is called a bit.

Related questions

the largest binary number is 1.84467440737e19. to figure this out you put 2 to the exponent of the certain amount of bits. Eg: 2^64 equals the binary number

The mantissa holds the bits which represent the number, increasing the number of bytes for the mantissa increases the number of bits for the mantissa and so increases the size of the number which can be accurately held, ie it increases the accuracy of the stored number.

15

Infinity - 1

1

The largest binary number is 1 1 1 1 1 1 1 1 1 1 . It is equivalent to the decimal number 1,023 .

The largest number is 11111111111111 which is 215 - 1. In decimal, that is 32767.

1,024 is the highest number 10 digits in binary can describe

The largest decimal number is binary 11111, which is decimal 31.

To achieve the answer to what the decimal equivalent of the largest binary number with five places (or bits) is, work this equation: The formula is 2_ -1 where n is the number of bits. That will get you where you need to be.

It is 1001

6