A calculator uses 9 bit binary numbers with one bit for the sign of the number, followed by 5 bits for mantissa, followed by 3 bits for the characteristic. • How does this calculator represent -30.5? ? ? ? ? ? ? • What interval of numbers are represented by this calculator with the code 1| 11101 | 111 <> <> <>

A calculator uses 9 bit binary numbers with one bit for the sign of the number, followed by 5 bits for mantissa, followed by 3 bits for the characteristic. • How does this calculator represent -30.5? ? ? ? ? ? ? • What interval of numbers are represented by this calculator with the code 1| 11101 | 111 <> <> <>

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 you have a 4-letter alphabet {A, B, C, D} and you wish to devise a binary code (with nospaces) for this alphabet such that no two words would be encoded the same. For example, if A = 1and B = 11, then AA and B would be encoded the same. It takes one second to transmit eachcharacter of the binary code (so, 101 would take 3 seconds and 110101 would take 6 seconds).(a) If each letter occurs with the same frequency, determine the most efficient code for the alphabetand explain why it is the most efficient.(b) Now suppose letter A occurs about 40% of the time, B and C both occur about 25% of thetime each, and C occurs about 10% of the time. Determine the most efficient code and explainwhy it is the most efficient.
In an 8-bit binary number, which is the most significant bit (MSB)? What is the decimal representation of each of the following unsigned binary integers? 00110101 b. 10010110 c. 11001100 What is the sum of each pair of binary integers? 10101111 + 11011011 10010111 + 11111111 01110101 + 10101100 Calculate binary 00001101 minus 00000111. How many bits are used by each of the following data types? word doubleword quadword double quadword What is the minimum number of binary bits needed to represent each of the following unsigned decimal integers? 4095 65534 42319 What is the hexadecimal representation of each of the following binary numbers? 0011 0101 1101 1010 1100 1110 1010 0011 1111 1110 1101 1011 What is the binary representation of the following hexadecimal numbers? 0126F9D4 6ACDFA95 F69BDC2A Whatistheunsigneddecimalrepresentationofeachofthefollowinghexadecimalintegers? 3A 1BF 1001…
1. Compact discs record two channels (left and right) of music at a sampling frequency of ??=44.1kHz for each channel. If each sample is encoded with 16 bits, and one byte is 8 bits, how many bytes are required to store 48.1 seconds of music? 2. Consider a system that uses 8-bit ASCII codes to encode letters. How long (in microseconds) will it take to transmit the bit sequence encoding Hello-World! if we use a bit time of 4 samples per bit, and transmit samples at a rate of 1MHz? 3. The ASCII table below gives the ASCII codes for common alphanumeric characters and symbols listed from MSB to LSB. What is the bit sequence encoding the message 113? Assume that we transmit the codes of each character in sequence with the LSB first.
In a Digital Logic examination, you are given two signed integers in different number systems. A= (64)16 B= -(103)8Determine their values in the decimal system AN, b) Find the value of n, the shortest word-length of a computer using two’s complement representation which can represent all these numbers. Find the largest and thesmallest numbers that can be represented. c) Give the n-bit two’s complement representations of the two numbers, where n isvalue determined in b.
Is the set of infinite bit strings with an equal number of 0s and 1s countable or uncountable?Is the set of infinite bit strings with an equal number of 0s and 1s countable or uncountable?
a) A fixed-point binary number system has 5 whole bits and 3 fractional bits. What is the range of numbers in binary that can be represented in this format? What is the decimal value of the largest number that can be represented? b) A fixed-point binary number system has 4 whole bits and 12 fractional bits. Show the (4-hexit) hexadecimal representation of the following decimal numbers 0.375, - 1.33, and 1/40 in this finite format. Do not show recurring sequences. c) Assume a 16-bit floating point format designed as follows: 4-bit signed exponent and 12-bit fraction. Normalization is strictly enforced. What is the hexadecimal representation of the 16-bit floating point format for 1/40?
The latest super-duper supercomputer has memory locations that are 64-bits wide. What is the largest unsigned integer that can be stored in one memory location? Suppose that we use sign-magnitude for storing negative numbers and dedicate one bit for a sign bit. What would be the largest POSITIVE integer that can be stored in a memory location.
Implement the Hamming Code error detection and correction algorithm for a group message to be transmitted over a network. Hamming code algorithm allows the receiver to detect errors that may have been introduced due to many factors such as noise, interference, and many others. -> Assume the following: 1. The sender message length is 2 bytes. The data transmitted to the user is the 2-byte data in addition to the parity bits. 2. The receiver must be able to detect and correct 1-bit error. Report :In the report you must include an overview of the Hamming code algorithm and you need to show: 1. The detailed calculation of the minimum number of parity bits needed for a message of 2-byte length. 2. Details on how sender generates the parity bits. 3. Details on how thew receiver detects and corrects a 1-bit error. THANKS., PLEASE GIVE DETAILED DESCRIPTION.
A string is called a palindrome if it reads the same when reversed. That is, the string x1 x2 ... xn is a palindrome if x1 x2 ... xn = xn ... x2 x1. The bit strings 11011 and 01011010 are palindromes.The bit strings 1011 and 01111 are not. How many bit-strings of length 7 are palindromes?
n alternative to hexadecimal notation for representing bit patterns is dotted decimal notation in which each byte in the pattern is represented by its base ten equivalent. In turn, these byte representations are separated by periods. For example, 12.5 represents the pattern 0000110000000101 (the byte 00001100 is represented by 12, and 00000101 is represented by 5), and the pattern 100010000001000000000111 is represented by 136.16.7. Represent each of the following bit patterns in dotted decimal notation. 0000111100001111 001100110000000010000000 0000101010100000
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
Suppose we use a machine that represents integers in 9 bits. Our unsigned integers actlike what set of modulo numbers? (Hint: When counting up, where does a 9 bit numberreset to zero.)