Using 64-bit IEEE 754 DOUBLE precision floating point with one(1) sign bit, eleven (11) exponent bits...

Using 64-bit IEEE 754 DOUBLE precision floating point with one(1) sign bit, eleven (11) exponent bits and fifty-two (52) mantissa bits, what is the decimal value of: 0xBFE4000000000000

Expert Solution

Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from hexadecimal to binary
Converting BFE4000000000000 to binary
B => 1011
F => 1111
E => 1110
4 => 0100
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
So, in binary BFE4000000000000 is 1011111111100100000000000000000000000000000000000000000000000000
1011111111100100000000000000000000000000000000000000000000000000
1 01111111110 0100000000000000000000000000000000000000000000000000
sign bit is 1(-ve)
exp bits are 01111111110
   => 01111111110
   => 0x2^10+1x2^9+1x2^8+1x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+1x2^1+0x2^0
   => 0x1024+1x512+1x256+1x128+1x64+1x32+1x16+1x8+1x4+1x2+0x1
   => 0+512+256+128+64+32+16+8+4+2+0
   => 1022
in decimal it is 1022
so, exponent/bias is 1022-1023 = -1
frac bits are 01

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1.01 * 2^-1
1.01 in decimal is 1.25
   => 1.01
   => 1x2^0+0x2^-1+1x2^-2
   => 1x1+0x0.5+1x0.25
   => 1+0.0+0.25
   => 1.25
so, 1.25 * 2^-1 in decimal is 0.625
so, 0xBFE4000000000000 in IEEE-754 double precision format is -0.625
Answer: -0.625

venereology answered 9 months ago

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.

IEEE 754 format of 32-bit floating-point is as follows. 1 8 (bits) 23 (bits) What’s stored...

IEEE 754 format of 32-bit floating-point is as follows. 1 8 (bits) 23 (bits) What’s stored in each region? What’s the bias value and how to get it? For decimal fraction: – 0.625, please represent it as given format (Note: you must show the specific procedure/stepsin order to get full credits. If you only present final result directly, you will only get half of the credits even if it is correct.).

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.

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

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

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?

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

Convert 1.67e14 to the 32-bit IEEE 754 Floating Point Standard, with the following layout: first bit...

Convert 1.67e14 to the 32-bit IEEE 754 Floating Point Standard, with the following layout: first bit is sign bit, next 8 bits is exponent field, and remaining 23 bits is mantissa field; result is to be in hexadecimal and not to be rounded up. answer choices 5717E27B 57172EB7 5717E2B7 C717E2B7 5771E2B7

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

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.

Question