Number System

  • Question: What is the binary equivalent of the decimal number 25?
    a) 11001
    b) 10101
    c) 11111
    d) 10001

  • Answer: a) 11001
    Explanation: To convert decimal 25 to binary, repeatedly divide by 2 and note the remainders from bottom to top: 25/2 = 12 R 1, 12/2 = 6 R 0, 6/2 = 3 R 0, 3/2 = 1 R 1, 1/2 = 0 R 1. The binary equivalent is 11001.
  • Question: What is the octal equivalent of the binary number 110101?
    a) 155
    b) 65
    c) 315
    d) 65.1

  • Answer: a) 155
    Explanation: Group the binary digits into sets of three from right to left (110 101), then convert each set to its decimal equivalent (6 5). The octal equivalent is 65.
  • Question: Which of the following is a valid hexadecimal digit?
    a) 8
    b) G
    c) 2F
    d) 14

  • Answer: c) 2F
    Explanation: Hexadecimal uses digits 0-9 and letters A-F, where A=10, B=11, ..., F=15. Therefore, 2F is a valid hexadecimal representation.
  • Question: What is the decimal equivalent of the hexadecimal number 1A?
    a) 16
    b) 26
    c) 21
    d) 31

  • Answer: b) 26
    Explanation: In hexadecimal, A is 10 and 1A is (1 * 16) + 10 = 16 + 10 = 26 in decimal.
  • Question: How many bits are required to represent 64 different values?
    a) 4
    b) 6
    c) 8
    d) 10

  • Answer: c) 8
    Explanation: To represent 64 values, you need 2^6 bits, as 2^6 = 64.
  • Question: What is the binary complement of 101001?
    a) 110110
    b) 010110
    c) 101001
    d) 010010

  • Answer: b) 010110
    Explanation: The 1's complement is obtained by changing 1s to 0s and 0s to 1s. The 2's complement is then obtained by adding 1 to the 1's complement.
  • Question: Which of the following is a power of 2?
    a) 15
    b) 16
    c) 25
    d) 32

  • Answer: b) 16
    Explanation: A power of 2 is a number that can be expressed as 2^n, where n is an integer. 16 is 2^4.
  • Question: What is the binary sum of 1011 and 1101?
    a) 11000
    b) 10110
    c) 10100
    d) 10010

  • Answer: d) 10010
    Explanation: Binary addition: 1011 + 1101 = 11000. Ignore the overflow and the correct sum is 0010, which is 10 in decimal.
  • Question: In the BCD (Binary Coded Decimal) system, what is the maximum decimal number that can be represented by a 4-bit binary code?
    a) 7
    b) 9
    c) 15
    d) 10

  • Answer: d) 10
    Explanation: BCD uses 4 bits to represent each decimal digit, so the maximum value with 4 bits is 9.
  • Question: Which of the following is not a valid binary number?

a) 101010
b) 11011.01
c) 111100
d) 1001

Answer: b) 11011.01

Explanation: Binary numbers only contain 0s and 1s. The presence of a decimal point makes the number invalid in the binary system.