For this problem we will use a hypothetical floating-point representation that is similar to IEEE-754. It uses 12 bits total, consisting of 1 sign bit, 5 exponent bits, and 6 mantissa bits. Convert -14.125 to this format. Write the three portions of the number below as binary strings using the appropriate number of bits. Sign (1 bit): Exponent (5 bits): Mantissa (6 bits):

For this problem we will use a hypothetical floating-point representation that is similar to IEEE-754. It uses 12 bits total, consisting of 1 sign bit, 5 exponent bits, and 6 mantissa bits. Convert -14.125 to this format. Write the three portions of the number below as binary strings using the appropriate number of bits. Sign (1 bit): Exponent (5 bits): Mantissa (6 bits):

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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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?
Our everyday number system in the UK and many other parts of the world is a base-10 system using Arabic numerals, namely the digits 0, 1, 9. Integers larger than 9 are represented by sequences of these elementary numerals. The numerical value encoded by such a sequence is determined by multiplying each numeral by 10k, where k is the position of the numeral counted from the back and starting at zero, and then summing together the contributions from all numerals. For example, 5207 = 5 × 10³ +2×10² +0×10¹ + 7×10⁰ The built-in int function in Python can take a string (type str) representing such a number and convert it to a Python integer (type int). Write a similar function base14_convert that takes a string and converts it to a Python integer according to the following number system: • the base is 14, i.e., the individual digits have to be multiplied by powers of 14 to obtain the numerical value; digits are represented by lower-case letters 'a', 'b', 'c', 'd', ..., i.e., 'a' is…
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
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?
4. The largest number with two-byte word length is: Ans: 5. How many lines needed in parallel representation to transimmit decimal integer values up to 17 in binary. Ans: is (2), -Q₁. 6. The base of the following is Ans:
The binary string 11001111101001 is a floating-point number expressed using the 14-bit simple model given in your text. What is its decimal equivalent? Note: in the 14-bit simple model, the left-most bit is the sign, followed by 5 bits for the exponent, followed by 8 bits for the mantissa (There are no implied bits). The exponent is in Excess 15 notation.
1. Generate the Hamming-code for the following 12-bit data string : 1 0 1 0 1 1 0 1 1 1 0 1 Show that the generated binary string does not have any errors.
Example: Assuming m-7 bits and using three of those bits for representing the fractional part, ( 1100.000 )2 ( 0110.000 )2 ( 0011.000 )2 ( 0001.100 )2 ( 0000.110 )2 ( 0000.011 )2 (12)10 %3D (12)10 / 2 (6)10 (6)10 /2 (3)10 (3)10 /2 (1.5)10 (1.5)10 / 2 (0.75)10 (0.75)10 / 2 (0.375)10 In this case, each successive division by two has shifted the binary sequence to the right by one bit.
Write down the bit pattern in the fraction assuming a fl oating point format that uses Binary Coded Decimal (base 10) numbers in the fraction instead of base 2. Assume there are 24 bits, and you do not need to normalize. Is this representation exact?
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 are the smallest positive number and the largest positive number that can be represented in this format? Write them in exponential notation.
We are given a number 0b1100_0000 represented in a 8-bit system. Prob 2. Answer the following questions: . What is the value in decimal if this is an unsigned number? . What is the value in decimal if this is a signed number? • If we extend (type case) this number to a 16-bit system as an unsigned number, what will it be in hexadecimal? • If we extend (type case) this number to a 16-bit system as a signed number, what will it be in hexadecimal?
Convert the decimal number -43.68 to a floating-point number expressed in the 14-bit simple model given in your textbook. Note: in the 14-bit simple model, the left-most bit is the sign, followed by 5 bits for the exponent, followed by 8 bits for the mantissa (There are no implied bits). The exponent is in Excess 15 notation. 101011.1010