Given below are two statements: Statement I: (1011101)2 = (135)8 Statement II:…
2023
Given below are two statements:
Statement I: (1011101)2 = (135)8
Statement II: (71)8 = (111001)2
In the light of the above statements, choose the correct answer from the options given below.
Answer: A. Both Statement I and Statement II are true — ConceptTo convert a positional numeral in base b to decimal, multiply each digit by b raised to its place value, counting from 0 at the right. A binary or…
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is true but Statement II is false
- D.
Statement I is false but Statement II is true
Attempted by 22 students.
Show answer & explanation
Correct answer: A
Concept
To convert a positional numeral in base b to decimal, multiply each digit by b raised to its place value, counting from 0 at the right.
A binary or octal equality is true when both representations give the same decimal value.
Application
For Statement I, (1011101)2 = 1×26 + 0×25 + 1×24 + 1×23 + 1×22 + 0×21 + 1×20 = 64 + 16 + 8 + 4 + 1 = 93. Also, (135)8 = 1×82 + 3×81 + 5×80 = 64 + 24 + 5 = 93. Thus Statement I has equal values on both sides.
For Statement II, (71)8 = 7×81 + 1×80 = 56 + 1 = 57. Also, (111001)2 = 1×25 + 1×24 + 1×23 + 0×22 + 0×21 + 1×20 = 32 + 16 + 8 + 1 = 57. Thus Statement II has equal values on both sides.
Cross-check
Grouping binary digits in sets of three from the right gives 001 011 101 = 135 in octal and 111 001 = 71 in octal. Therefore, both Statement I and Statement II are true.