Question

Convert the binary number (01011.1011)2 into decimal.

(a) (11.6875)10

(b) (11.5874)10

(c) (10.9876)10

(d) (10.7893)10

I got this question in class test.

Enquiry is from Number System in portion Number System and Codes of Digital Circuits

Answer 1

Right choice is (a) (11.6875)10

The best I can explain: Binary to Decimal conversion is obtained by multiplying 2 to the power of base index along with the value at that index position.

(01011)2 = 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 11

              (1011)2 = 1 * 2^-1 + 0 * 2^-2 + 1 * 2^-3 + 1 * 2^-4 = 0.6875

             So,   (01011.1011)2 = (11.6875)10.