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ITC544 | Data Representation and Digital Logic

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Added on  2019-10-31

ITC544 | Data Representation and Digital Logic

   Added on 2019-10-31

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Assignment 1: Data Representation and Digital LogicITC544NAME: ID:
ITC544 | Data Representation and Digital Logic_1
1.a.0 01111110 10100000000000000000000In IEEE-754 single precision format, starting from the left, first bit denotes the sign ofthe decimal number (positive or negative), next 8 bits represents the exponent of the number and remaining bits represents the mantissa.Following the standards:Here, first bit (sign bit) is 0, therefore, we can say that the number is positive.Next 8 bits are 01111110, therefore, each bit is multiplied with a power of 2 and is then added together.01111110 --- 0*27 + 1*26 + 1*25 + 1*24 + 1*23 + 1*22 + 1*21 + 0*20= 126For the exponent, 127 is subtracted from the result.126 – 127= -1Exponent is -1Now, next bits are 10100000000000000000000, in this last 20bits are 0 which will have no effect on the mantissa as it will result to 0. Therefore,1.101 is considered.Multiplying with the exponent1.101 * 10-1= 0.1101For the decimal number, the bits are multiplied with the negative power of 2 at the right side of decimal point and positive power of 2 at the left side.0.1101 --- 0*20 + 1*2-1 + 1*2-2 + 0*2-3 + 1*2-4 = 0.8125 b.“word” of 5 bits is numbers which can be represented in maximum 5bits. Therefore, in general, these numbers start from 00000 (all 0’s) and end at 11111 (all 1’s). But fordifferent magnitudes, they vary.i.Binary --- 01111 – 11111Decimal --- -15 – 15 ii.Binary --- 10000 – 01111Decimal --- -16 – 15 iii.Binary --- 10001 – 01111Decimal --- -17 – 152. Page 1 of 5
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