Hexadecimal Number System - Free MCQ Practice Test with solutions, GATE

• Here we have to perform an XOR operation on two Hexadecimal numbers.
• The boolean expression for XOR is 
• The truth table for XOR is:
  
• Means A and B are the expressions given to us in Hex code. So, we need to find the binary equivalent of the Hexadecimal numbers. This is because these codes will be executed in 1 and 0 in the CPU.
• The following table is to be memorized in order to convert Hexadecimal to Binary:
  
• Therefore, (4AC0)₁₆ = 0100101011000000
• And (B53F)₁₆ = 1011010100111111
• Now follow the Truth Table to perform the operation on every bit in XOR gate:
  
• So the result obtained is (1111111111111111)₂ which is the Binary Equivalent of (FFFF)₁₆ (using the table given above).
• Hence the correct answer is FFFF.

Concept: 

• Hexa decimal division process:
• Step 1: Convert the given hexadecimal numbers to decimal.
• Step 2: perform division operation to the decimal numbers.
• Step 3: Convert the result to requires number system.

Calculation:

Convert the given hexadecimal numbers to decimal and perform division operation and for the remainder obtained, convert that remainder into hexadecimal.

(9)₁₀ in hexa decimal form is represented as shown

⇒ (9)₁₀ = 0 × 16¹ + 9 × 16⁰ = 09H

∴ The remainder is 09H

Hexadecimal number to decimal number

Binary to Hexadecimal conversion table:

Concept:-

Hexadecimal number system: Hexadecimal is a radix-16 or base-16 number system, while in our day-to-day life in computers and digital logic we use a base-2 (binary) number system, but it is visually more efficient to use base-16 (Hexadecimal) number system.

Decimal number system: The most common base-10 number system that we use frequently.

In general

Where a_n = Hexadecimal number at the nth place.

The above expansion of a number in any radix r, always gives back the decimal equivalent of the number.

Calculation:
Given,
Hexadecimal number is (B2F8)₁₆
Expanding according to equation 1,

So, the decimal equivalent of the given hexadecimal number is (45816)₁₀.

Concept:

The radix or base of a number system is defined as the number of different digits which can occur in each position in the number system

Application:

For hexadecimal number system base is 16 hence there are 16 different digits from (0 - F)
Any number containing digit greater than F is invalid hexadecimal number.
So, GFAB is invalid hexadecimal number

• Hexadecimal numbers are used extensively in microprocessor work. 
• The hexadecimal number system has a base of 16.
• After reaching 9 in the hexadecimal system, we continue as A, B, C, D, E, F. 
• For converting a decimal number to a hexadecimal number, the number is successively divided by 16 with remainders occupying the successive positions from the right.

The procedure is exactly similar to the procedure for converting a decimal number to binary. 

 

where, N = number, B = base, A_n = (n + 1)^th digit in that base. 
Converting hexadecimal to the decimal.
Let hexadecimal number =11
So, N = 1*16¹ + 1*16⁰ = 1*16 + 1*1 =16 +1 = 17
The decimal number 11 is smaller than the hexadecimal number 11.

Convert Decimal to Hex:

• Decimal to hexadecimal conversion can be achieved by applying the repeated division and remainder algorithm.
• Decimal to Hex step by step Method:
• If the given decimal number is less than 16, the hex equivalent is the same. Remember that the letters A, B, C, D, E, and F are used for the values 10, 11, 12, 13, 14, and 15, convert accordingly
• For example, the decimal number 15 will be F in Hex.
• If the given decimal number is 16 or greater, divide the number by 16.
• Write down the remainder.
• Divide the part before the decimal point of your quotient by 16 again. Write down the remainder.
• Continue this process of dividing by 16 and noting the remainders until the last decimal digit you are left with is less than 16.
• When the last decimal digit is less than 16, the quotient will be less than 0 and the remainder will be the digit itself.
• The last remainder you get will be the most significant digit of Hex value while the first remainder from Step 3 is the least significant digit.

Concept:

• Hexadecimal number: In this, value of the base is 16. Each digit is represented by 4-bit binary no.
• Octal number: For octal number, value of base is 8. Each digit of an octal number is represented by 3-bit binary no.

Explanation:

Octal number = 657
Binary representation for this number (each digit of a octal number is converted into 3 binary bits) 
So, 657 in binary is equivalent to 110 101 111
Now group this binary number into 4 bits starting from right to left. 
i.e. 0001 1010 1111
Hexadecimal representation for this number is : 1AF

Binary Representation of (430.25)₈ is:
(430.25)₈ = (100011000.010101)₂
converting the above binary representation into hexadecimal,we get

Therefore Correct answer is Option 2

The system uses 10 numerical digits and 6 alphabets –0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, A, B, C, D, E, F.

• The Hexadecimal numbering system uses the Base of 16 system and is a popular choice for representing long binary values because their format is quite compact and much easier to understand.
• Being a Base-16 system, the hexadecimal numbering system, therefore, uses 16 (sixteen) different digits with a combination of numbers from 0 through to 15. In other words, there are 16 possible digit symbols.
• However, there is a potential problem with using this method of digit notation caused by the fact that the decimal numerals of 10, 11, 12, 13, 14 and 15 are normally written using two adjacent symbols.
• To get around this tricky problem hexadecimal numbers that identify the values of ten, eleven, twelve, thirteen, fourteen, and fifteen are replaced with capital letters of A, B, C, D, E and F respectively.