Computer Number System Questions with Solutions
Computers store and process all data in binary, using only the digits 0 and 1. This topic covers the four number systems used in computing: binary (base 2), octal (base 8), decimal (base 10) and hexadecimal (base 16, using digits 0 to 9 and letters A to F). It covers converting numbers between these systems, binary arithmetic (addition, subtraction, multiplication and division), and complements (1's and 2's complement) used to represent negative numbers. The fastest conversions go through binary. Each octal digit equals a group of three binary digits, and each hexadecimal digit equals a group of four. To convert decimal to binary, divide by 2 repeatedly and read the remainders from bottom to top. Character encoding schemes such as ASCII and Unicode are also covered at a basic level. Practise the computer number system questions below, each with a step-by-step conversion.
- Q101.
Which of the following represents ?
A. B. C. D.easyAsked in NIMCET 2019View solution āŗ - Q102.
In an 8-bit representation of a computer system, the decimal number 47 has to be subtracted from 38. The result in binary 2's complement is _________
A. 11110111B. 10001001C. 11111001D. 11110001easyAsked in NIMCET 2019View solution āŗ - Q103.
The quotient, if the binary number 11010111 is divided by 101, is ______
A. 101101B. 101010C. 111001D. 101011easyAsked in NIMCET 2024View solution āŗ - Q104.
Consider the following 4-bit binary numbers represented in the 2's complement form: 1101 and 0100. What would be the result when we add them?
A. 0001 and no overflowB. 1001 and an overflowC. 0001 and an overflowD. 1001 and no overflowmediumAsked in NIMCET 2024View solution āŗ - Q105.
Given that numbers A and B are two 8-bit 2's complement numbers with A = 11111111 and B = 11111111, the sum A + B is ______
A. 00000010B. 11111100C. 11111110D. 00000000easyAsked in NIMCET 2024View solution āŗ - Q106.
Consider an arbitrary number system with independent digits 0, 1 and A. If we generate the first few numbers in sequence as 00, 01, 0A, 10, 11, 1A and this process is continued to generate the numbers, then the position of 10A is ______
A. 15B. 10C. 12D. 9mediumAsked in NIMCET 2024View solution āŗ - Q107.
The range of the exponent E in the IEEE 754 double precision (binary64) format is ______
A. B. C. D.mediumAsked in NIMCET 2024View solution āŗ - Q108.
Let the given numbers 11001, 1001 and 111001 correspond to the 2's complement representation. Then with which one of the following decimal numbers do the given numbers match?
A. -6, -6 and -6 respectivelyB. -7, -7 and -7 respectivelyC. -25, -9 and -57 respectivelyD. 25, 9 and 57 respectivelymediumAsked in NIMCET 2024View solution āŗ - Q109.
What is the equivalent decimal value of the unsigned binary number 10101.10101?
A. 125.25B. 51.125C. 25.375D. 21.65625easyAsked in NIMCET 2025View solution āŗ - Q110.
Consider a 9-bit representation. Which of the following correctly gives the smallest number that can be represented in (i) 1's complement and (ii) 2's complement?
A. (i) ā256, (ii) ā255B. (i) ā255, (ii) ā255C. (i) ā255, (ii) ā256D. (i) ā256, (ii) ā256mediumAsked in NIMCET 2025View solution āŗ - Q111.
Which of the following statements about ASCII and Unicode is correct?
A. Unicode is backward compatible with ASCII and includes all ASCII characters in its encoding.B. ASCII uses 16 bits per character, while Unicode uses only 7 bits.C. Unicode and ASCII are completely different and share no common characters.D. ASCII can represent more characters than Unicode because it uses fewer bits per character.easyAsked in NIMCET 2025View solution āŗ - Q112.
What is the hexadecimal representation of the decimal number 265?
A. 0x100001001B. 0x109C. 0x411D. 0x190easyAsked in NIMCET 2025View solution āŗ