# ITC544 Assignment on Data Representation and Digital Logic

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## ITC544 Assignment on Data Representation and Digital Logic

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Full student NameStudent IDSubject Code (ITC544)Assessment Item Number and Name(Assignment 1: Data Representation and Digital Logic)Page 1 of 5
Question 1(a)A computer uses IEEE-754 single precision format to represent floating point. What value (indecimal) does the computer represent if the floating point is represented using the followingbinary digits. (6 marks)0 01111110 10100000000000000000000SolutionTo convert from IEEE-754 to decimal, it is important to note that,(i)The first term determines the sign of the number, the second term determines theexponent, while the third term determines the fraction or the mantissa. (ii)When the first term is 0 it is a positive number, if it is a 1 it is a negative number.(iii)Determine the exponent by converting the binary octet to decimal value. Since, thebinary set is a single-precision number, subtract the exponent from the bias of 127.(iv)The third term or the mantissa is converted to a fraction in base ten. (v)The resultant syntax of conversion is,(1)signbit(1+fraction)sexponentbiasThe binary digits are signed 0 meaning it is a positively signed number.The next section is 01111110 which is converted to decimal to represent the number,011111102=12610The mantissa is given by,.101000000000000000000002=.524288010e=1261012710=110¿(1)0(1+0.625)21Page 2 of 5

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