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# Lab03_Floating_Point_Number_Answer_11 - 3 SignBit Exponent...

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CC2202-Computer System Architecture Lab 3 Answer Page 1 Subject : CC2202 : Computer System Architecture Lab/Tutorial : Session 3 (Answer) Floating Point Number Subject Lecturer : Steven Chan Number System 1 ) Convert 27.1875 10 to its binary and hexadecimal equivalent Bin: 11011.0011 Hex: 1B.3 16 2) Convert F.4 to its decimal equivalent. F 16 = 15 10 0.4 16 = 4 x 16 -1 = 0.25 10 F.4 16 = 15.25 10 3) Represent the decimal values 26 and –123 as 8-bit numbers in the following binary formats: a) Sign and magnitude: 26: 0 0011010 -123: 1 1111011 b) 2’s complement: 26: 0 0011010 -123: 1 0000101 4) Given the following binary numbers in 2s-complement representation. Perform the operations and indicate if there are any results overflowed. a) 010110 - 011111 b) 111110 - 100101 =010110+100001 =111110 + 011011 =110111 =011001 010110 111110 + 100001 +011011 1 10111 011001

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CC2202-Computer System Architecture Lab 3 Answer Page 2 5) Given the following Standard for 32-bit floating point number, as shown in figure
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Unformatted text preview: 3, SignBit Exponent Significand 1 bit 8 bits 23 bits Figure 3 Note that: 1) Implied bit is used in the significand 2) The Exponent is 127 biased a) Find the decimal value of 1 100 0101 0 010 1000 0000 0000 0000 0000 MSB (sign bit): 1 => -ve Biased Exponent = 1000 1010 2 = 138 10 Exponent =138 10-127 10 =11 10 Significant = .0101 2 (not including the implied bit) Significant = 1.0101 2 (including the implied bit) Significant in decimal = 1 10 +0.25 10 +0.0625 10 = 1.3125 10 Value= -1.3125 X 2 11 = -2688 10 b) Find the floating point representation of 13.625 10 13 10 = 1101 2 0.625 10 = 0.5 10 +0.125 10 = 0.101 2 Normalization 13.625 10 = 1101.101 2 =1.101101 x 2 3 Therefore MSB (sign bit) = 0 Exponent = 3 10 + 127 10 = 130 10 = 1000 0010 2 Significand = 1.1011 0100 0000 0000 0000 000 2 Significand = 1011 0100 0000 0000 0000 000 2 (implied bit omitted) Ans: 0100 0001 0101 1010 0000 0000 0000 0000...
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