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# Fractional Numbers and Blackboard Notation.?

Any help with how to solve this question

### 1 Answer

- az_lenderLv 72 months ago
(a) The binary expansion of 37 is 100101, and the binary expansion of 0.8 is

0.1100110011001100..., so 37.8 is

100101.1100110011001100 ...

(b) Hexadecimal expansion of 37.8 is 25.CCCC...

(c) Normalized binary expansion is

1.00101110011001100...

with exponent 5.

(d) Now look at the normalized binary expansion and just translate it directly to hex:

1.2E6666...

with exponent 101 ( = 5). The selected exponent is for a binary representation, and I believe that is customary (not an exponent for hex directly).

(e) Sorry, I don't know the "blackboard" system.