1 Use the 16 bit format depicted below referred to as fpx to

1) Use the 16 bit format depicted below (referred to as fpx) to perform the following:

a) Convert ED80 from fpx to decimal

b) Convert 7440 from fpx to decimal

c) Convert 1.745 * 10 ^-3 from decimal to fpx

d) Convert -0.111 * 2^4 from binary to fpx

15                14 13 12 11 10                                   09 08 07 06 05 04 03 02 01 00

Solution

a)

ED80 = 1110 1101 1000 0000

Sign bit (S) = 1
Exponent bits (e) = 11011 = 27
Fraction bits (f) = 01 1000 0000

Equivalent decimal number = (-1)^S * 2^(e-b) * (1.f)
= (-1)^1 * 2^(27-15) * (1.0110000000)
= - 2^12 * (1.0110000000)
= - (1011000000000)
= - (4096+1024+512)
= - 5632.

b) 7440= 0111 0100 0100 0000

Sign bit (S) = 0
Exponent bits (e) = 11101 = 29
Fraction bits (f) = 00 0100 0000

Equivalent decimal number = (-1)^S * 2^(e-b) * (1.f)

(-1)^0 * 2^(29-15)*(1.0001000000)

=2^(14)*(1.0001000000)

100010000000000=17408

c) 1.745*10^-3=0.001745

0.001745*2=0.00349 generates 0

0.00349*2=0.00698 generates 0

0.00698*2=0.01396 generates 0

0.01396*2=0.02792 generates 0

0.02792*2=0.05584 generates 0

0.05584*2=0.11168 generates 0

0.11168*2=0.22336 generates 0

0.22336*2=0.44672 generates 0

0.44672*2=0.89344 generates 0

0.89344*2=1.78688 generates 1

0.78688*2=1.57376 generates 1

0.57376*2=1.14752 generates 1

0.14752*2=0.29504 generates 0

0.29504*2=0.59008 generates 0

0.59008*2=1.18016 generates 1

1.745*10^-3=(000000000111001000)₂

_{normalize= 1.1100 0100 0000 0000*2^-10}

_{mantissa 1100 0100 0000 0000}

exponent is (-10+50176)=50166= 1100001111110110

1100001111110110=C3F6

sign bit =0;

os 1.745*10^-3 =7

d) -0.111*2^4

sign bit =1

mantissa 1110 0000 0000 0000 =57344

exponent (4+57344)=57348=1110000000000100

11110000000000100=1E004