What is the biggest number that can be represented with 24 bits? How many bits r

Question

What is the biggest number that can be represented with 24 bits? How many bits required to represent hexadecimal numbers? Why we use Hexadecimal? Give some example where we use Hexadecimal numbers. h. What are the numbers/symbols in octal number system? How many bits required to represent octal numbers? i. What are numbers/symbols in binary number system? Give an example where we use binary number system. What is bytes? j. Compile a list of at least 20 everyday objects that incorporate microcontrollers, microprocessors or digital signal processors.

Explanation / Answer

1. What is the biggest number that can be represented with 24 Bits?

Ans : The range of unsigned integers that can be represented in 24 bits is 0 to 16,777,215. The range of signed integers that can be represented in 24 bits is 8,388,608 to 8,388,607.

2. How many bits required to represent hexa decimal numbers? Why we use Hexadecimal? Give some examples of using Hexadecimal Number?

Ans.    The hexadecimal numeral system, also known as just hex, is numerical made up of 16 symbols (base 16). The standard numeral system is called decimal (base 10) and uses ten symbols: 0,1,2,3,4,5,6,7,8,9. Hexadecimal uses the decimal numbers and includes six extra symbols. There are no symbols that mean ten, or eleven etc. so these symbols are letters taken from the alphabets A, B, C, D, E and F. Hexadecimal A = decimal 10, and hexadecimal F = decimal 15.

            As each hexadecimal digit represents four binary digits (bits) it allows a more human-friendly representation of binary- code values. One hexadecimal digit represents a nibble (4 bits), which is half of an octet or byet (8 bits). For example, a single byte can have values ranging from 00000000 to 11111111 in binary form, but this may be more conveniently represented as 00 to FF in hexadecimal.

Humans mostly use the decimal system. This is probably because humans have ten fingers (ten digits). Computers however, only have on and off, called a binary digit (or bit, for short). A binary number is just a string of zeros and ones: 11011011, for example. For convenience, engineers working with computers tend to group bits together. In earlier days, such as the 1960's, they would group 3 bits at a time (much like large decimal numbers are grouped in threes, like the number 123,456,789). Three bits, each being on or off, can represent the eight numbers from 0 to 7: 000 = 0; 001 = 1; 010 = 2; 011 = 3; 100 = 4; 101 = 5; 110 = 6 and 111 = 7. This is called octal

As computers got bigger, it was more convenient to group bits by four, instead of three. The additional bit can be either on or off, a 0 or a 1. So this doubles the numbers that the symbol would represent. This is 16 numbers. Hex = 6 and Decimal = 10, so it is called hexadecimal. Four bits is called a nibble (sometimes spelled nybble). A nibble is one hexadecimal digit, and is written using a symbol 0-9 or A-F. Two nibbles is a bytes (8 bits). Most computer operations use the byte, or a multiple of the byte (16 bits, 24, 32, 64, etc.). Hexadecimal makes it easier to write these large binary numbers.

3. What are the numbers and symbols in octa number system? How many bits are required to represent a octa number?

Ans:    The octal number system, or oct for short, is the base 8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: (00)1 001 010, corresponding the octal digits 1 1 2, yielding the octal representation. Octal was an ideal abbreviation of binary for these machines because their word size is divisible by three (each octal digit represents three binary digits). So four, eight or twelve digits could concisely display an entire machine word

4. What are the numbers and symbols used in binary system? where do we use binary system? what is bytes?

Ans. binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one) Computers use binary numbers because they have circuits which are either on or off, which gives them two states to work from to make calculations and run processes. The two-digit, or base 2, number system is much easier for the computer to process with the circuits they have. The byte is a unit of digital information that most commonly consists of eight bits.

5. Compile a list of at least 20 everyday objects that incorporate microcontrollers, microprocessors or digital signal processors?

Ans: Cell phone, Mp3 player, Microwave oven, PDA Automobiles (many!), Desktop computer, Disk drives, Digital cameras, Dishwashers Washing machines, Ovens, DVD players, CD players, Stereo receivers, Electronic musical keyboards, Computer keyboards, Computer mice Network routers / wireless access points, Laser Printers, Ink Jet printer

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