Question
Download Solution PDFIf (L) represents a number L in base-M number system, then identify the correct descending order of the following numbers A-D when converted to decimal number system.
(A) (10110.11)2
(B) (110.2)4
(C) (32.5)8
(D) (14.6)16
Choose the correct answer from the options given below:
Answer (Detailed Solution Below)
Option 1 : (C), (A), (B), (D)
Detailed Solution
Download Solution PDFThe correct answer is - (C), (A), (B), (D)
Key Points
- Conversion to decimal number system
- (A) (10110.11)₂
- Convert binary to decimal:
(10110.11)2=1×24+0×23+1×22+1×21+0×20+1×2−1+1×2−2 - Decimal equivalent:
16+4+2+0.5+0.25=22.75
- Convert binary to decimal:
- (B) (110.2)₄
- Convert quaternary to decimal:
(110.2)4=1×42+1×41+0×40+2×4−1 - Decimal equivalent:
16+4+0+0.5=20.5
- Convert quaternary to decimal:
- (C) (32.5)₈
- Convert octal to decimal:
(32.5)8=3×81+2×80+5×8−1 - Decimal equivalent:
24+2+0.625=26.625
- Convert octal to decimal:
- (D) (14.6)₁₆
- Convert hexadecimal to decimal:
(14.6)16=1×161+4×160+6×16−1 - Decimal equivalent:
16+4+0.375=20.375
- Convert hexadecimal to decimal:
- (A) (10110.11)₂
Additional Information
- Base-N Number Systems
- Each digit in a number represents a coefficient of a power of the base.
- The base determines the number of different digits, including zero, that a positional numeral system uses to represent numbers.
- Common bases include:
- Binary (Base-2): Uses digits 0 and 1.
- Quaternary (Base-4): Uses digits 0, 1, 2, and 3.
- Octal (Base-8): Uses digits 0 through 7.
- Hexadecimal (Base-16): Uses digits 0 through 9 and letters A through F.
- Conversion Methods
- To convert from any base to decimal, multiply each digit by its base raised to the power of its position, and sum the results.
- Fractional parts involve negative powers of the base.