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Digital Logic Part 1 Number conversions IEEE-754 number

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Added on  2020-03-28

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There is an invisible leading bit that is not stored in the memory but is placed as the first bit, Therefore, in the given number 0 01111110 10100000000000000000000 Equivalents of “word” using 5 bits Signed number One’s complement Two’s complement For a signed number using 5 bits the range is such that, power 6 5 4 3 2 1 0 Base 2 1000000 100000 10000 1000 100 01 1 Base 10 64 32 16 8 4 2 1 Five bits are

Digital Logic Part 1 Number conversions IEEE-754 number

   Added on 2020-03-28

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Student nameSubject codeLecturerDate of submissionData Representation and Digital LogicPart 1(a)Number conversionsIt is important to note that there are two kinds of zeros: +0 and -0The value of an IEEE-754 number is computed as shown,sign∗2exponent∗mantissaThe sign is stored in bit 32. The exponent can be computed from bits 24 to 31 by subtracting the exponent obtained from 127. The mantissa is also referred to as the significand or fraction. The significand is stored in bits of 1-23. There is an invisible leading bit that is not stored in the memory but is placed as the first bit,Therefore, in the given number0 01111110 101000000000000000000000−positivesignednumber01111110=12610exponent=12610−12710=−110¿(−1)0∗(1+0.625)∗2−1¿1.625∗12¿0.812510(b)Equivalents of “word” using 5 bits (i)Signed number(ii)One’s complement(iii)Two’s complementPage 1 of 4
Digital Logic Part 1 Number conversions IEEE-754 number_1
For a signed number using 5 bits the range is such that,power6543210Base 21000000100000100001000100011Base 106432168421Five bits are represented by the highlighted section,The signed magnitude, one’s complement and two’s complement are represented as shown below,Signed Magnitude¿+1510¿−1510¿011112¿111112One’s complementtherangeis[−15,15]10¿111112¿100002Two’s complementtherangeis¿[−16,15]10¿011112¿100002Part 2(a)Part aMain entrance CSU door activationThe lock system has a 24 hour clock that times the locking schedule.9:00 am to 12:00 noon main entrance door active1:00 pm to 4:00 pm main entrance door activeFour inputs namely W, X, Y, Z are to be usedThe circuit diagram is as shown below,Page 2 of 4
Digital Logic Part 1 Number conversions IEEE-754 number_2

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