Convert the following binary and hexadecimal num- bers to floating point format. Assume a binary format consisting of a sign bit (negative = 1), a base 2, 8-bit, excess-128 exponent, and 23 bits of mantissa, with the implied binary point to the right of the first bit of the mantissa. a. 110110.011011,
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- 5. Find 10011001 is an 8-bit binary sequence. Find the decimal value it represents if it was in unsigned and signed magnitude. Suppose this representation is excess notation, find the decimal value it represents?Perform floating points binary arithmetic addition on the following binary numbers as represented in a non- standard form. Assume 4 binary digits for significand A 1 bit 8 bits 9 bits + 1 bit 8 bits 9 bits 01111000 100111000 0111110 0 000101000 What is the value of biased exponent of A, Eb_a? What is the floating point representation of A? What is the value of biased exponent of B, Ep_B? What is the floating point representation of B? Sum A+B (Normalized)?Consider a 16-bit binary floating point number representation system: + SE E EEEE m m m m The first bit of the exponent is dedicated to its sign. Assume that the mantissa must start with a '1'. Use this system to answer the following questions: 1. What is the smallest (magnitude) number that can be represented with this system? 2. Calculate the relative round-off error introduced when this system tries to represent e = 2.718281828459045235360287 .. using rounding.
- Consider an 8-bit floating point format. In this representation 4 bits are reserved for the mantissa and 3 bits are reserved for the exponent and 1 bit is reserved for the sign of the number. The exponent of the number is stored with a bias = 3. Express the decimal number 4.75 in this 8 bit floating point format. Write down the next bigger representable number in decimal base. B If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.75 Express the decimal number 4.75 in this 8 bit floating point format. [10] b) Write down the next bigger representable number in decimal base. [7.5] c) If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.75Convert the following unpacked Binary Coded Decimal (BCD) encodings to their decimal values. Note: Spaces are placed between each 4-bit sequence to make the binary sequence more readable and decrease the likelihood of a mistake. a) 0000 0001 0000 1001 0000 0111 b) 0000 0011 0000 0010 0000 0100Floating-Point Representation. What is the floating-point value for binary 4. a) 11000010100000 using the simple model (14-bit format, 5 bits for the exponent with a bias 15, a normalized significand of 8 bits, and a single sign bit for the number)?
- MCQS so now carefully read the question and give the most appropriate answer. a) If the following binary number were to be represented in the IEEE-754 single precision floating point format, then what would be the value of the exponent field in binary. 10111010.0101 b) If the following binary number were to be represented in the IEEE-754 single precision floating point format, then what would be the binary value stored in the sign bit. 10111010.0101 c) Convert the decimal number 1.1 into its equivalent binary representation. d) The maximum value in hexadecimal that can be stored in a single byte is e) If the following binary number were to be represented in the IEEE-754 single precision floating point format, then what would be the binary value that would be stored in the significand part. 10111010.0101 f) The sum of the following two octal values, 77 and 56 can be expressed in octal as:Please help me with those questions 1. a. Convert 113 (in base 10) to a binary number using the unsigned 8-bit binary representation. b. .Convert 1001 1010 to an integer assuming that the binary sequence uses the unsigned 8-bit binary representation. Present your answer using the usual sign-magnitude base 10 representation. c.Convert the binary sequence 1010 0001 to a decimal integer assuming that the binary sequence uses the two's complement 8-bit binary representation. Present your answer using the usual sign-magnitude base 10 representation. c. Add 0100 1011 and 1011 0111 assuming that the binary number represents unsigned 8-bit integers. Present your answer as an 8-bit binary number using unsigned 8-bit representation. d. Convert the decimal -107 (written using the usual signed-magnitude base 10 representation) to a signed 8-bit binary number using the two's complement representation.1. Determine the 32-bit binary representation for floating point numbers inthe form± I.F x be where I is the interger part,F is the fraction,b is the base, ande is the exponent.Using this format, represent the number 0.00001011001100101 as a 32bit floating point number. (b) ) During the process of digital sampling, data can be lost due to aliasing.Analyse this problem and provide at least two possible solutions. Also,determine the rate at which a signal should be sampled, if the highestfrequency is 50MHz (c) ) An 9-bit binary number is used to represent an analog value in the rangefrom -10oC to 100oC, determine the resolution of the system andinterprete your result.
- a) Determine the 32-bit binary representation for floating point numbers in the form± I.F x be where I is the interger part,F is the fraction,b is the base, ande is the exponent.Using this format, represent the number -1.00011011101 x 225 as a 32 bit floating point number. b) During the process of digital sampling, data can be lost due to aliasing. Analyse this problem and provide at least two possible solutions. Also, determine the rate at which a signal should be sampled, if the highest frequency is 60MHz. c) In your own words, discuss the relationship between the hexadicimal number system and the binary number system. Use this relationship to convert the following hexadecimal values to binary.i) 5BC916 ii) 6EF816 iii) 8A4D16 iv) 9ED516Please solve and show all work. Thank you. What is 5ED4 - 07A4 when these values represent unsigned 16-bit hexadecimal numbers? The result should be written in hexadecimal. Show your work. What decimal number does the bit pattern (0C000000)16 represent if it is a floating-point number? Use the IEEE 754 standard. Write down the binary representation of the decimal number 63.25, assuming the IEEE 754 double precision format. What are the corresponding MIPS instructions to this C code: C code: float f2c (float fahr) { return ((5.0/9.0)*(fahr - 32.0));} if fahr in $f10, result in $f2, literals in global memory space.Show Steps Please 20. Suppose we have just found yet another representation for floating point numbers. Using thisrepresentation, a 12-bit floating point number has 1 bit for the sign of the number, 4 bits forthe exponent and 7 bits for the mantissa, which is normalized as in the Simple Model so thatthe first digit to the right of the radix points must be a 1. Numbers in the exponent are in signed2's complement representation. No bias is used and there are no implied bits. Show therepresentation for the smallest positive number this machine can represent using the followingformat (simply fill in the squares provided). What decimal number does this equate to?