Question

Machine Organization

3. Write the decimal equivalents for these IEEE floating point numbers. a. 0 1000000000000000000000000000000 b. 1 10000011 00011000000000000000000 4. Translate the following ASCII codes into strings of characters byinternreting

Answer 1

a) o 1000 0000 0000 0000 0000 0000 0000000 pooo 00000 0000 0000 0000 0000 000 0000 Fraction bits - exponent Siegn a bite bits Sign bita ospositive 1 → Negative * Decimal value in positive, Because Sign bit is O. If sign bit is a, we will get negative Decimal value. * bits to convert exponent Step 2: Decimal (1000 0000), o exponent bits 32 CS caht canner CS Scannez wioxź toxż tox { + oxż toxot oxé tox

= 128 + 07 OTO + Ororoto - 128 (1000 0000), (128) step 3: exponent bias= 127. exponent (e)= 128 - exponent bias - 128-127 stepti Tate traction bits toooo 0000 0000 0000 0000 000 Fraction bits figured out the Fraction bits used mantisa -23 O X2 -2 --3 OX2 + 0x2 + OX 2 - 4 + 0X2+oX 2 t... Mantisa=9 CS Scanned Scanned with CamScanner

steps: (+) x ( 1+ M) x 2² S = sign bit-o es F1 )*(1+0) x2 (1= 1 1x (1) *2 = 2 ; Final watte Decimal value = 2 Answer = 2 / a Note : Any thing power o is En 28=2, 1952 Scanned with CamScanner

i 1000 0011 00011 000000000000000000 2 Stepat 1000 0011 00011 000000000000000000 exponent bits Fraction bits 10 Sign bit a E sign bit = 1, So value in Negative step 2: convert exponent bits decimal (1000 00l1). E = 1x2 +0x2+ox {totox ² +0x27 1x2'+ 1X2 - 128 +0+0+ OtoTOT 2+1 131 erpoorest bios = 127] - steps: exponent (et 131- ex ponent bias = 131-127 e 4 Scanned with CamScanner

traction bits to mantisa tep 4: convert no 0001 000000000000000000 = O 2 +OX 2+OX 2 + -4 x 2 + -5 x 2 -6 +OX 2 + TOA to Ototo+0.0625+0.0312570+ 0.06250 10.031 25 0.09375 Mantisa M= 0.09375 lei stup 5: Dec alue = Steps: Decimal value= (413** (11m)* 2 613** (1 +0.093 75 )* 2+ = -1 * (1009375)*16 CS Scanneal with 1* (17.5) = -17-5 CamScanner

Final Answer = -17-5 Note: get Sign bit is 1 , So @ will Negative decimal value Scanned with CamScanner