Question

This section of the examination tests your comprehension of the subjects covered in the module. 1. The IEEE 754 standard for representing real numbers is included in the data sheet, which is attached to the end of this paper. For the number 0.40625 a. What is the value of the sign bit? [1 Mark] b. What is the value of the exponential when expressed as an 8 bit signed integer using twos complement? [3 Marks] c. What are the values of the bits that represent the significand? [2 marks]

Answer 1

© Let us understand the standard clearly - IEEE 754-1985 istardard. saya the following - Standard is vied to represent floating point representation ton numbers. exponent M Mantussa X ② Mantissa (called - For 32 bit number (single precision) 0.04.20*2 Sign, for which I bit is allocated (sign of number) bits. significand) is allocated 23 Exponent ment is allocated 8 bits poritive negative exponents are to be represented using 8 bits. So They decided to set a bias of 137 he eo 127 means le 128 neau So. exponent value = Letored value in Bolte and e=0 and 데 } -127 рьін 6 Normalized significand, which means most significant bit is always D. 0101inci V 8 23 always bi 68 sign Exponer . significand Number 0.40625 in Binary & 0.01101 → 0.01101 1.101 X 2 makan Normalized → Now exponent exponent = -2 aking So stored value - 2 + 127 125 0114 1101 significand = 101000...no 20 times sign bit o positive number CSscanned with CamScanner

Let us answer the questions now 9 sign bit co ** positive num number exponent n - -2 in two's com +2= 0000 0010 So here they are asking to represent oplement so we weget -2 => 1' complement 2 complement represent exponent on als exponents :g' bits 1111 1110 1111 1101 1111 1110 So. if we complement we get с Values of bits for significand are as same at we e found earlier significand 101 00000000000000000000 go total 32 bit number becomes 0 1111 1110 J 101 00000.00000 00000 0000 0 J Significand. sign exponent csscanned with CamScanner.

in summary

we have explained the standard

we have solved the given number and the questions asked