7. A pair of 7-bit floating point formats, based on the IEEE standard, is described below: (a) Format (a) has k = 3 and n = 4. The exponent bias is 3. Format (b) has k = 4 and n = 3. The exponent bias is 7. Convert the bit patterns below, given in format (a) to bit patterns in format (b). Convert exact values when possible, otherwise use the round-to-even rule. Also, write the values of each bit pattern, for the (a) and (b) formats. Write the values, in decimal, as rational numbers, or whole integers. Bits (a) Value Bits (b) Value 1 0111 000 011 0000 101 1010 110 1011 000 0011 1 (b) What is the smallest positive denormalized number in format (b)? What is the largest positive denormalized number in format (b)?

7. A pair of 7-bit floating point formats, based on the IEEE standard, is described below: (a) Format (a) has k = 3 and n = 4. The exponent bias is 3. Format (b) has k = 4 and n = 3. The exponent bias is 7. Convert the bit patterns below, given in format (a) to bit patterns in format (b). Convert exact values when possible, otherwise use the round-to-even rule. Also, write the values of each bit pattern, for the (a) and (b) formats. Write the values, in decimal, as rational numbers, or whole integers. Bits (a) Value Bits (b) Value 1 0111 000 011 0000 101 1010 110 1011 000 0011 1 (b) What is the smallest positive denormalized number in format (b)? What is the largest positive denormalized number in format (b)?

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

See similar textbooks

Similar questions

VI. Floating point representation Consider a 12-bit variant of the IEEE floating point format as follows: • Sign bit 5-bit exponent with a bias of 15. • 6-bit significand All of the rules for IEEE 754 Standard apply. Fill in the numeric value represented by the following bit patterns. You must write your number in decimal form (e.g. 0.0146485375, -0.0146485375). Bit Pattern 010011101110 111011101011 100101001111 001010111010 Numerical Value
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
True/False In Floating Point Addition, the exponents of the two numbers being added need to be made equal before the mantissa fields can be added, as this ensures that the bit positional values are now aligned
1. In a binary coded decimal (BCD) system, 4 bits are used to represent a decimal digit from 0 to 9. For example, 3710 is written as 00110111BCD. (a) Write 28910 in BCD (b) Convert 100101010001BCD to decimal (c) Convert 01101001BCD to binary (d) Explain why BCD might be a useful way to represent numbers
6. Assume we are using a simple model for floating-point representation similar to the one used in Chapter 2 of the textbook which has a 14-bit format, 5 bits for the exponent with a bias of 15 (not 16 as in the textbook), a normalized mantissa of 8 bits, and a single sign bit. Show how the computer would represent the numbers 12.125 using this representation.
1- Write the different numbers in base 10 a. (FA) 16 b. (101.011) 2 2. Write the following number in base 2 a. (123.22) 10 3. Realize the following additions in a 8 bits system using the 2's complement representation a. S1 = -51 +27 b. S2-51 - 27 c. S351 - 27 4. Realize the following addition using BCD representation a. S = 833 + 573
For 10 bits floating point representation using: seeeefffff, what is the bias for denormalized numbers? A. 7 B. 6 C. 4 D. 3 E. 2 What is the range of integers that can be represented using 8 bits 2's complement? A. -127 to 127 B. -128 to 127 C. -127 to 128 D. 0 to 255 E. 0 to 256
Consider a floating point format that uses 4 digits in the significand including the leading 1. In other words, the significand is given by (1.d₁d2d3)2. (a) Assuming you have enough bits in the exponent, compute fl(25.75) for this floating-point format. (b) How many significant digits is fl(25.75) accurate to? (c) How many bits are needed in the exponent such that computing fl(25.75) will not result in nu- merical overflow?
We are using the simple model for floating point representation which is a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit. Show step by step how the computer would represent the following numbers using this floating- point format | a. -6.47510 i. Convert it into a binary number ii. Normalize this binary number iii. Fill up the fields
In the Hamming coding system (7.3), its representation is expressed as 3 control (test) bits and 7 total bits (data+control bits).In the literature, control bits are represented as (cl, c2, c3, or (pl, p2, p3, .) The bit string sent by encoding with Hamming coding (15,4) is on the receiving side, It is retrieved as 001100101100 (pl.p2.dll). According to this bit sequence;Which option is given according to the control bits (p1.p2.p3.p4) sequence of the received bit sequence?A 0110B 1100C 1001D 0011E 0010
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.