Number System in Digital Logic : Practice MCQ Questions & Answers with Explanations

The correct option is (1) Concept:- In the number system, we know hexadecimal is base 16 and octal is base-8 Calculation: To convert hexadecimal D.C to octal, First, convert D.C16 into decimal = D16 = D × 160 + C × 16-1 = 13.7510 Now, we have to convert 13.7510 to octal 13/8 = 1 with remainder 5 1/8 = 0 with remainder 1 13 = 15 ----(1) For converting decimal fraction 0.75 to octal number, 0.75 × 8 = 6 + 0 0.75 = 0.6 ---(2) ∴ 13.7510 = 15.68 ------ [ from (1) and (2) Hence, hexadecimal number D.C converted to octal is equals: 15.6

The correct answer is: option 4 Key Points Explanation: Convert the binary number and the hexadecimal number to decimal: 11012 = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13 A516 = 10×16¹ + 5×16⁰ = 160 + 5 = 165 Sum: 13 + 165 = 178 Therefore the correct decimal value of the sum is 178,

The correct answer is ASCII Code. Key Points ASCII (American Standard Code for Information Interchange) is a character encoding standard used to represent text in computers, telecommunications, and other devices. Each character, including letters, numbers, and symbols, is assigned a unique numeric value that is stored as a binary number in memory. For example, the character 'A' is represented by the numeric value 65 in ASCII, which is stored in binary as 01000001.

Calculations: Following choices are: 46, 51, 60, 42 1) 46 - The sum of digits is 10, not 6, so it can't be this. 2) 51 - The tens digit isn't double the ones digit, so it can't be this. 3) 60 - This exceeds the upper limit of less than 6 tens, so it can't be this.

Concept used: The successor of any number is the value that comes immediately after the original number. Calculation: The successor of 10999999 is (10999999 + 1) = 11000000 ∴ The correct answer is 11000000

Concept: The closure property of the multiplication of natural numbers states that the multiplication of two or more natural numbers always result in a natural number. Explanation: Hence, two or more natural numbers multiplied results in a natural number. For example, 5 × 2= 10, is a natural number.

Given: While calculating the value of 95 × 103, a student writes 95 × 103 = 10000 + 10a - 15. Concept used: ⇒ (a - b) × (c + d) = (a × c) + (a × d) - (b × c) - (b × d) Calculation: We can write 95 × 103 = (100 - 5) × (100 + 3) ⇒ (100 ×100) + (100 × 3) - (5 × 100) - (5 × 3) ⇒ 10000 + 300 - 500 - 15 ⇒ 10000 - 200 - 15 We can write it as, ⇒ 10000 - 20 × 10 - 15 Compare with given statement, 10000 + 10a - 15. ⇒ a = - 20 ∴ Option 3 is correct.

Concept used: XL represents 40 in Roman numerals, LX represents 60, and LXXIV represents 74. Calculations: To find the value of (XL + LX - LXXIV), we first perform the addition and subtraction inside the parentheses, as follows: XL + LX - LXXIV = 40 + 60 - 74 Simplifying the addition and subtraction gives: = 100 - 74 = 26 = XXVI

Given: Distance = 2,896,819,200,000 metres Concept used: The standard form of a number is expressed in the powers of 10. Solution: Distance = 2,896,819,200,000 metres = 2.8968192 x 1012 m Hence, the correct option is 1.