converting decimal to IEEE-754 format

Question

I am trying to convert 30.125 into 10 bit floating number. 1 sign bit, 5 exponent bit with bias of 15 and 4 Mantisa bit. I came up with the below solution in IEEE-754 format which is correct.

S E Mantissa 0 10011 1110

Then part of the question asks what decimal value is represented by the above floating number and the correct answer was 30. can How did they get 30?

Malcolm McLean · Accepted Answer · 2017-04-15 18:00:24Z

1

There's an implict 1, so if the exponent is zero (15 because of the bias), the mantissa is 1.xxxx, so here 1.111 - remember the point is a binary point. However the exponent is 19. Take away the bias of 15, and it is 4.

So the binary number is 11110 - shift the binary pointy right 4 places. 2 + 4 + 8 + 16 = 30.

answered Apr 15, 2017 at 18:00

Malcolm McLean

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3 Comments

blor Over a year ago

Thanks for the explanation, can you explain how many bits in the exponent and mantissa we would need if we wanted to store the the additional 0.125?

Patricia Shanahan Over a year ago

@blor Decimal 30.125 is binary 11110.001, 8 significant bits. You need to store 7 of them, so you would need a 7 bit significand. The exponent is unchanged.

blor Over a year ago

@PatriciaShanahan Thanks but the correct answer was given as 8 bits not 7.

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