Learn how decimal numbers are represented in floating-point format.
Your decimal number is:
Convert the positive version of the number above into a 9-bit fixed-point binary format (1 sign bit, 4 integer bits, 4 fractional bits). The sign bit for a positive number is 0.
Correct! Now, since the original number was negative, convert the positive fixed-point representation to its two's complement form.
(i) Flip all the bits.
Positive Form:
(ii) Now, add 1 to the result.
Normalize the binary pattern by shifting the dot. For positive numbers (MSB=0), the form should be 0.1.... For negative numbers (MSB=1), it should be 1.0....
Almost there! Now, construct the final floating-point number.
• The Mantissa is formed from the normalized number (e.g., from 1.011... or 0.101...).
• The Exponent is the shift count, converted to 4-bit two's complement.
Mantissa (8 bits)
Exponent (4 bits)