Question

The given hexadecimal number (1E.53)16 is equivalent to ____________

(a) (35.684)8

(b) (36.246)8

(c) (34.340)8

(d) (35.599)8

I had been asked this question in my homework.

Question is taken from Number System in section Number System and Codes of Digital Circuits

Answer 1

The correct option is (b) (36.246)8

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

(1E.53)16 = (0001 1110.0101 0011)2

= (00011110.01010011)2

= (011110.010100110)2

= (011 110.010 100 110)2

= (36.246)8.