# Perform the following base conversions using

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2.Perform the following base conversions using subtraction or division-remainder:a.58810= _________b.225410= ________c.65210=________d.310410= ________Ans.3579a. 2102103b. 330045c. 16217d. 42289
______________________________________________________________________________3.Convert the following decimal fractions to binary with a maximum of six places to the rightof the binary point:a.26.78125b.194.03125c. 298.796875d. 16.1240234375Ans.a. 11010.11001b. 11000010.00001c. 100101010.110011d. 10000.000111______________________________________________________________________________4.Convert the following decimal fractions to binary with a maximum of six places to the rightof the binary point:a.25.84375b. 57.55c. 80.90625d. 84.874023Ans.a. 11001.11011b. 111001.100011c. 1010000.11101d. 1010100.110111______________________________________________________________________________5.Represent the following decimal numbers in binary using 8-bit signed magnitude, one'scomplement and two's complement:a. 77b. -42c. 119d. –107Ans.a.Signed magnitude: 01001101One's complement: 01001101Two's complement: 01001101b.Signed magnitude: 10101010One's complement: 11010101Two's complement: 11010110c.Signed magnitude: 01110111One's complement: 01110111Two's complement: 01110111
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Chapter 31 / Exercise 18
Contemporary Abstract Algebra
Gallian
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______________________________________________________________________________
6.Using a "word" of 3 bits, list all of the possible signed binary numbers and their decimalequivalents that are representable in:______________________________________________________________________________
7.Using a "word" of 4 bits, list all of the possible signed binary numbers and their decimalequivalents that are representable in:
______________________________________________________________________________8.From the results of the previous two questions, generalize the range of values (in decimal)that can be represented in any givenxnumber of bits using:a. Signed magnitudeb. One's complementc. Two's complement
Ans.a.-(2x-1-1) to +(2x-1-1)b.-(2x-1-1) to +(2x-1-1)c.-(2x-1) to +(2x-1)______________________________________________________________________________9.Given a (very) tiny computer that has a word size of 6 bits, what are the smallest negativenumbers and the largest positive numbers that this computer can represent in each of thefollowing representations?a.One's complementb.Two's complementAns.______________________________________________________________________________
Page 4Last Updated: November 200310. You have stumbled on an unknown civilization while sailing around the world.The people,who call themselves Zebronians, do math using 40 separate characters (probably becausethere are 40 stripes on a zebra).They would very much like to use computers, but wouldneed a computer to do Zebronian math, which would mean a computer that couldrepresent all 40 characters.You are a computer designer and decide to help them.Youdecide the best thing is to use BCZ, Binary Coded Zebronian (which is like BCD except it
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Term
Spring
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Binary numeral system, Hamming Code, Parity bit, Ans a
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Chapter 31 / Exercise 18
Contemporary Abstract Algebra
Gallian
Expert Verified