Which of the following three numbers (A-C) in decimal, octal and hexadecimal…
2022
Which of the following three numbers (A-C) in decimal, octal and hexadecimal notations, respectively, is/are equivalent to (11011001)2 in binary notation?
(A) (217)10
(B) (661)8
(C) (D9)16
Choose the correct answer from the options given below:
Answer: D. A and C only — CONCEPTA positional numeral in base b has value equal to the sum of each digit multiplied by the corresponding power of b. Binary can also be converted to…
- A.
A only
- B.
B only
- C.
A and B only
- D.
A and C only
Attempted by 14 students.
Show answer & explanation
Correct answer: D
CONCEPT
A positional numeral in base b has value equal to the sum of each digit multiplied by the corresponding power of b. Binary can also be converted to octal or hexadecimal by grouping bits from the right in groups of three or four.
APPLICATION
Convert the binary number to decimal: 110110012 = 1×27 + 1×26 + 0×25 + 1×24 + 1×23 + 0×22 + 0×21 + 1×20 = 128 + 64 + 16 + 8 + 1 = 217.
The decimal candidate 21710, represents the same value.
For octal, group the bits as 011 011 001. These groups are 3, 3 and 1, so 110110012 = 3318, not 6618. The octal candidate does not represent the same value.
For hexadecimal, group the bits as 1101 1001. These groups are D and 9, so 110110012 = D916. The hexadecimal candidate represents the same value.
CROSS-CHECK
D916 = 13×16 + 9 = 208 + 9 = 217, while 6618 = 6×64 + 6×8 + 1 = 433. The independent decimal check confirms the decimal and hexadecimal candidates.
Therefore, the equivalent numbers are 21710 and D916.