Consider the following floating point representation where each number has 2 exponent bits and 5 fraction bits. The exponent bias is 1. Round each number to have 3 fraction bits. Apply round-to-even and round-toward-zero modes. a. 1 10 11100 b. 0 00 00101 c. 1 01 10101 i. Can you see a pattern for rounding floating point numbers when the number of exponent bits are intact?

Suppose that we use the floating-point format with 12 decimal digits, SEEEMMMMMMMM, to rep- resent a real number, where S is the digit to represent the sign of the mantissa (use 0 for pos- itive and 5 for negative), EEE are the 3 digits to represent the exponent in excess-500 format, MMMMMMMM are the 8 digits to represent the magnitude of the mantissa, and the decimal point of the mantissa is right to the left of MMMMMMMM (i.e., SEEEMMMMMMMM representing the real number ±0.MMMMMMMM × 10EEE-500) What is the second largest positive number that can be represented in this for- mat? How much less is this number compared to the largest number? Can you represent a number located somewhere between the largest number and the second largest number?

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.

For example: Binary value of character ‘B’ from ASCII table is 01000010Dataword is 1000010 Even Parity Bit is 0 Codeword: 10000100 Even Parity – Complete the following table using Even Parity Character  Binary Datawordfrom ASCII table(7-bit value) Parity BitValue TransmittedCodeword  ReceivedCodewordat Receiver Check ifthecodewordisrejected t 1010100     10101101   h 1101000     11010000   i 1101001     11010010   s 1110011     11100110

Show that the negation of Tmin is Tmin. You can pick any Tmin (Tmin for 4-bits, Tmin for 5 bits etc). Also, explain why the negation of Tmin is Tmin. (Hint: ‘negation’ and ‘not operator’ is not the same thing

When providing a base-ten block representation for the number 3.59, James uses 2 flats, 13 Rods, and 29 cubes. Is this an acceptable representation, if it is not explain why, if it is tell me the unit that James is using.

The following is a string ASCII characters whose bit patterns have been converted into hexadecimal for compactness:           CD 69 E4 54 E5 72 6D Of the eight bits in each pair of digits, the left most is a parity bit and the remaining bits are the ASCII code. Convert the string to bit form and decode the word in ASCII. What is the parity for each letter of the word?

Assume we have a 2's complement system with an 8-bit whole number part and a 2-bit fractional part. Find a decimal representation of 2's complements binary number 1110 0010.01 it expects a numeric entry. It will automatically suppress leading and trailing zeros. It will display your answer with commas every third digit.

1) Find the equivalent decimal value of the following floating-point representation using IEEE 754 standard single-precision (32-bit floating-point number with bias = 127)  1 0111 1111 1110 0000 0000 0000 0000 000 (The quiz is expecting a decimal numeric entry. It will automatically suppress leading and trailing zeros. It will display your answer with commas every third digit.)   2) Find an IEEE 754 floating-point representation of -74.2 decimal number. Enter 32 bits without a space.  (The quiz is expecting a fill in the blank text string in the entry box and grades on an exact match with the expected result. The answer should be formatted as a 32-bit IEEE 745 binary number representation)

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?