a newer version of IEEE 754 defines a half precision floating point format that is only...

a newer version of IEEE 754 defines a half precision floating point format that is only 16 bits wide. the left most bit is still the sign bit. the exponent is 5 bits wide and has a bias of 15, and the fraction is 10 bits long. A hidden 1 is assumed similar to single and double precision formats. what is the bit pattern to represent -0.5 using this format?

Expert Solution

1011100000000000

Explanation:
-------------
-0.5
Converting 0.5 to binary
   Convert decimal part first, then the fractional part
   > First convert 0 to binary
   Divide 0 successively by 2 until the quotient is 0
   Read remainders from the bottom to top as
   So, 0 of decimal is  in binary
   > Now, Convert 0.50000000 to binary
      > Multiply 0.50000000 with 2.  Since 1.00000000 is >= 1. then add 1 to result
      > This is equal to 1, so, stop calculating
   0.5 of decimal is .1 in binary
   so, 0.5 in binary is 00000000.1
-0.5 in simple binary => .1
so, -0.5 in normal binary is .1 => 1. * 2^-1

16-bit format:
--------------------
sign bit is 1(-ve)
exponent bits are (15-1=14) => 01110
   Divide 14 successively by 2 until the quotient is 0
      > 14/2 = 7, remainder is 0
      > 7/2 = 3, remainder is 1
      > 3/2 = 1, remainder is 1
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 1110
   So, 14 of decimal is 1110 in binary
frac/significant bits are 0000000000

so, -0.5 in 16-bit format is 1 01110 0000000000

venereology answered 9 months ago

Convert 1101.11011101 x 223 to IEEE Standard 754 for single-precision floating-point binary format. Convert the IEEE...

Convert 1101.11011101 x 223 to IEEE Standard 754 for single-precision floating-point binary format. Convert the IEEE Standard 754 number 11001010100011010101000000000000 to its decimal equivalent.

A) Convert 1101.11011101 x 223 to IEEE Standard 754 for single precision floating-point binary format. B)...

A) Convert 1101.11011101 x 223 to IEEE Standard 754 for single precision floating-point binary format. B) Convert the IEEE Standard 754 number 11001010100011010101000000000000 to its decimal equivalent.

Convert 0xCD001234 from IEEE-754 hexadecimal to single-precision floating point format. Please show every single detail for...

Convert 0xCD001234 from IEEE-754 hexadecimal to single-precision floating point format. Please show every single detail for upvote. Please do not answer otherwise.

For IEEE 754 single-precision floating point, what is the hexadecimal representation of 27.101562? A. 35CCD001 B....

For IEEE 754 single-precision floating point, what is the hexadecimal representation of 27.101562? A. 35CCD001 B. 2F5C10D0 C. 41D8D000 D. 7DCA1111 E. None of the above

Using IEEE 754 single precision floating point, write the hexadecimal representation for each of the following:...

Using IEEE 754 single precision floating point, write the hexadecimal representation for each of the following: a. Zero b. -2.0 (base 10) c. 256. 0078125 (base 10) d. Negative infinity

Convert 0.875 to an IEEE 754 single-precision floating-point number. Show the sign bit, the exponent, and...

Convert 0.875 to an IEEE 754 single-precision floating-point number. Show the sign bit, the exponent, and the fraction. Convert -3.875 to an IEEE 754 double-precision floating-point number. Show the sign bit, the exponent, and the fraction Convert the IEEE 754 single-precision floating-point numbers 42E4800016 and 0080000016 to their corresponding decimal numbers.

write value of PI(3.14159) in IEEE-754 single-precision format

Given the following 32-bit binary sequences representing single precision IEEE 754 floating point numbers: a =...

Given the following 32-bit binary sequences representing single precision IEEE 754 floating point numbers: a = 0100 0000 1101 1000 0000 0000 0000 0000 b = 1011 1110 1110 0000 0000 0000 0000 0000 Perform the following arithmetic and show the results in both normalized binary format and IEEE 754 single-precision format. Show your steps. a) a + b b) a × b

Express the following two base 10 numbers in binary using the IEEE 754 single-precision floating point...

Express the following two base 10 numbers in binary using the IEEE 754 single-precision floating point format (i.e., 32 bits). Express your final answer in hexadecimal (e.g., 32’h????????). a) 68.3125 b) -19.675

verilog code to implement 32 bit Floating Point Adder in Verilog using IEEE 754 floating point...

verilog code to implement 32 bit Floating Point Adder in Verilog using IEEE 754 floating point representation.

Question