Question

Convert the following floating-point number (stored using IEEE floating-point standard 754) to a binary number in...

Convert the following floating-point number (stored using IEEE floating-point standard 754) to a binary number in non-standard form.

1100_0100_1001_1001_1000_0000_0000_0000

Homework Answers

Answer #1
1 10001001 00110011000000000000000
sign bit is 1(-ve)
exp bits are 10001001
Converting 10001001 to decimal
   10001001
   => 1x2^7+0x2^6+0x2^5+0x2^4+1x2^3+0x2^2+0x2^1+1x2^0
   => 1x128+0x64+0x32+0x16+1x8+0x4+0x2+1x1
   => 128+0+0+0+8+0+0+1
   => 137
in decimal it is 137
so, exponent/bias is 137-127 = 10
frac bits are 00110011

IEEE-754 binary value is 1.frac * 2^exponent
IEEE-754 binary value is 1.00110011 * 2^10 = 10011001100

let's convert this to decimal
Converting 10011001100 to decimal
10011001100
=> 1x2^10+0x2^9+0x2^8+1x2^7+1x2^6+0x2^5+0x2^4+1x2^3+1x2^2+0x2^1+0x2^0
=> 1x1024+0x512+0x256+1x128+1x64+0x32+0x16+1x8+1x4+0x2+0x1
=> 1024+0+0+128+64+0+0+8+4+0+0
=> 1228

Answer in binary:   -10011001100
Answer in decimal:  -1228
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
How do you convert a decimal like 4.9219 into binary? (assuming 32-bit IEEE 754 floating point...
How do you convert a decimal like 4.9219 into binary? (assuming 32-bit IEEE 754 floating point format)
Convert the number 425.6 to the IEEE-754 32-bit floating point format. Don't use cheet
Convert the number 425.6 to the IEEE-754 32-bit floating point format. Don't use cheet
Convert the following binary floating point number 100101.1001010101 using IEEE-756 single precision representation Plz show work,...
Convert the following binary floating point number 100101.1001010101 using IEEE-756 single precision representation Plz show work, thanks!
Represent the following decimal numbers using IEEE-754 floating point representation. please show all work i. -0.75...
Represent the following decimal numbers using IEEE-754 floating point representation. please show all work i. -0.75 ii. 0 iii. - infinity iv. 23 v. 10.25
Assuming a 5-bit IEEE (754 standard) floating-point format where 1 bit is used for the sign,...
Assuming a 5-bit IEEE (754 standard) floating-point format where 1 bit is used for the sign, 3 bits for the exponent, and 1 bit for the fraction, write the formulas for the exponent E, the significand M, the fraction f, and the value V for the quantities that follow and also describe the bit representation. Please show all steps to receive full credit. The number 5.0 The largest odd integer that can be represented exactly The reciprocal of the smallest...
Using the IEEE single-precision floating point representation, find the decimal number represented by the following 32-bit...
Using the IEEE single-precision floating point representation, find the decimal number represented by the following 32-bit numbers, each expressed as an 8-digit hex number. Express your answer using decimal scientific notation. (a) (C6500000)16 (b) (31200000)16
Given the following pair of decimal numbers: A = 2.6125 x 101 and B = 4.150390625...
Given the following pair of decimal numbers: A = 2.6125 x 101 and B = 4.150390625 x 10-1 a) Compute the binary representation of both A and B using the IEEE-754 single precision floating- point format. b) Compute A+B in binary using the IEEE-754 single precision floating-point format.
Using the 32-bit binary representation for floating point numbers, represent the number 10111001100112 as a 32...
Using the 32-bit binary representation for floating point numbers, represent the number 10111001100112 as a 32 bit floating point number.
Consider IEEE standard single-precision floating-point format. What is the distance between the largest value and the...
Consider IEEE standard single-precision floating-point format. What is the distance between the largest value and the 2nd largest value?
Matlab uses IEEE double precision numbers: 64-bit floating point representation 1 bit : sign 11 bits:...
Matlab uses IEEE double precision numbers: 64-bit floating point representation 1 bit : sign 11 bits: exponent 52 bits: mantissa. Calculate largest number that can be stored accurately Calculate smallest number (x>0) that can be stored accurately Calculate the machine epsilon Show all work step by step and explain calculations Now calculate the largest number and smallest number for a 10 bit floating point (1 bit for the sign, 4 bits exponent and 5 bits mantissa)