Question

The octal number (651.124)8 is equivalent to ______

(a) (1A9.2A)16

(b) (1B0.10)16

(c) (1A8.A3)16

(d) (1B0.B0)16

The question was posed to me in an international level competition.

I'd like to ask this question from Number System topic in portion Number System and Codes of Digital Circuits

Answer 1

Right choice is (a) (1A9.2A)16

The best I can explain: First, the octal number is converted to it’s equivalent binary form, by writing the binary equivalent of each digit in form of 3 bits. Then, the binary equivalent bits are grouped in terms of 4 bits and then for each of the 4-bits, the respective digit is written. Thus, the hexadecimal equivalent is obtained.

(651.124)8 = (110 101 001.001 010 100)2

= (110101001.001010100)2

= (0001 1010 1001.0010 1010)2

= (1A9.2A)16.