Question

Convert the following from the floating point representation to a decimal (base 10) representation using the format in 5.19 of your text: 10010111010010100011011010101011

Answer 1

Convert the following from the floating point representation to a decinal (base 10) Given nomben is 10010111010010100011011010o101011 the give number is 3a- bil flonting point numbur -» from IEEE 754 the starting bit is sign bit here stanting is 1 is -ve number So, our decimal equivalent -> And the next 8-bits cene exponent bis 0010 L110 convert the above capònent to decimal ( o0101110)a 46 bias In IEEE 754 we have to remove Cz 46 -127 -81 Now Remaining bits is mantissa Convert mantissa to decimal 0100 011O 1101 0101 011 1001 a- -4 Value e -1) -14 +2 -18 -20 -22 -23

After computing the value of manhissa is m 0.57979333401 given number is divided this way 00101110 1001010001101to0101011 T. Sign bit - ve mantissa = 0 5797933340) -81 Now conveiting we have to substitute value in general decimal form. to decimal (~1) x CI+mantissa) x 2e 3- sign bit M z mantiss a exponential. ->(-1) x (1+ 0.579793334-01)x2 18- X 1.5797933401 x => ithe Required decimal equivalent is get By Solving above we -6.63387de -25 This is the desired decimal -6.533872e-25