Question

5) What is the possible range of numbers that can be represented with the following a. 12 bits in binary b. 6 digits in hex c. 6 digits in decimal

Answer 1

12 bits in binary:

• One binary digit is equal to a bit. There are only two possible states in bit, 0 and 1.
• This number system is having 2 as it's base.
• 8 bits=1 byte.
• 12 bits means value from 0 to (2^12)-1 i.e from 0 to 4095 , the range of numbers will be [-4095 to 4095] i.e with having both negative, positive and a value of Zero. It can also be written as Signed and 111111111111​ (4095 in binary representation).

6 digits in Hexa:

• The number system which is made up of 16 symbols is called Hexadecimal Number system. It uses decimal numbers and extra 6 symbols. The number system having 16 as it's base is called as Hexadecimal number system which is generally called as "Hexa".
• There are no symbols which represents 10, 11 etc., in this system, 6 symbols are represented as follows with the English Alphabets.
• A=decimal 10,B= decimal 11,C= decimal 12, D=decimal 13, E=decimal 14, F=decimal 15.
• In hexadecimal each digit can have 16 values.
• so 6 digits can have range from 0-5.

6 digits in Decimal:

• Any number system is defined by it's base.
• The number system having 10 as it's base is called as Decimal.
• It consists of 10 single digits .
• For 6 digits the range of number is from 0-5.