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,

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,

Systems Architecture

7th Edition

ISBN:9781305080195

Author:Stephen D. Burd

Publisher:Stephen D. Burd

Chapter8: Data And Network Communication Technology

Section: Chapter Questions

Problem 31VE

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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 - 4.75
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Floating-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.
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2. For the following questions, use an 8-bit (IEEE 754 normalized) floating-point format with 1 sign bit, 4 exponent bits, and 3 significant bits. Note that this format is similar to the 32-bit and 64-bit formats in terms of the meaning of fields and special encodings. The leading significant 1 is assumed and the exponent field employs an excess-7 coding; which means you subtract 7 from the unsigned exponent. a. Encode the following numbers into the 8-bit floating-point format : Encode the following numbers into the 8-bit floating-point format : i. 0.00110112c ii. 16.010sm iii. 0b0.01011011U (0b prefix = binary, U suffix = unsigned) b. Decode the following floating-point number into its decimal value: 1 1010 101 c. Which number in the following pairs are greater in value: i. 0 1000 100 and 0 1000 111 ii. 1 1100 100 and 1 1100 101 d. Maximum Positive Value (excluding positive infinity) e. Minimum Positive Value (excluding zero and subnormal numbers)
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?