b) (i)Is it possible to design a 3-bit binary code to represent each of the 7 digits of the base-7 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? (ii)Is it possible to design a 3-bit binary code to represent each of the 8 digits of the base-8 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? [Remember: a code is self-complementing when the complementary digits in base 7 encode into complementary triplets in the 3-bit representation; for instance BCD is not self-complementing, for 0 and 9 are complementing, but 0000 and 1001 are not; the 2421 code is self-complementing]

b) (i)Is it possible to design a 3-bit binary code to represent each of the 7 digits of the base-7 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? (ii)Is it possible to design a 3-bit binary code to represent each of the 8 digits of the base-8 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? [Remember: a code is self-complementing when the complementary digits in base 7 encode into complementary triplets in the 3-bit representation; for instance BCD is not self-complementing, for 0 and 9 are complementing, but 0000 and 1001 are not; the 2421 code is self-complementing]

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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Computer Science Question
2. Assume we are using the simple model for floating-point representation as given in this book (the representation uses a 16-bit format, 5 bits for the exponent with a bias of excess-15, a normalized mantissa of 10 bits, and a single sign bit for the number): Show how the computer would represent the numbers a) +3.53125 and -3.34375 using this floating-point format. a) +3.53125 b)-0.09375
If the 5-bit 2’s complement of X is equal to 01010, then
2. Determine the representation of the following decimal numbers in the floating point number system of a 32-bit word length microcomputer: (a) (7.90625) 10 and (b) (-12.875)10-
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H - For the IEEE 754 single-precision floating point, write the hexadecimal representation for the following decimal values: (i)–1.0 (ii)– 0.0 (iii)256.015625
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Chapter 2: Practice Problems 1. Assume we are running code on a 8-bit machine using two's complement arithmetic for signed integers. A "short" integer is encoded using 4 bits. Fill in the empty boxes in the table below. The following definitions are used in the table: short sy = -3; int y = sy; int x = -17; unsigned ux = x Note: You need not fill in entries marked with "-" Only accepted format for binary representation (use 8-bits): 00000000, 11111111 Only accepted format for hexadecimal representation: 4D, EF, FF Expression Binary Zero ux y X >> 2 Tmax Tmax+Tmin Tmin - 1 Decimal 0 -3 00110010 Hexadecimal
(3) The IEEE 754 standard specifies a single-precision binary floating-point format (binary32) as having 1 bit for sign bit, 8 bits for exponent, and 23 bits for fractions (mantissa). Given the conversion formula as follows, value2 = (-1)'31 × (1. b22b21 . bo)2 × 2(b30b29 .b23)2-127 ... (a) encode -2.2510 ; (b) decode 0 1000 0001 011 0000 0000 0000 0000 00002
Problem 1 Considering the floating-point number format used by the IBM System/360-370 series, determine the total number of different normalized numbers that the 32-bit version of this format can represent.
11] Encode Decimal '127 7/8' into Fixed Point Binary. Express your answer in Hex. 12] Encode Decimal '-92 13/32' into IEEE 754 Floating Point. Express your answer in Hex.