Question

Express the decimal value-4.9375 ten as IEEE-754 Single Precision Floating Point, or else state “NOT POSSIBLE” if the value cannot be represented (e.g. underflow condition). No credit will be given if your answer is stated in any format besides hexadecimal or “NOT POSSIBLE”, accordingly. Note: Only the non-fractional quantity“1” is noted in Yellow Font, in accordance with Syllabus page 11.

Answer 1

binary representation of 9375 is 10010010011111

In single precision 32 bits are used

1 bit for sign and denoted as S

8 bits for exponent and denoted as E

23 bits for mentisa and denoted as M

Normalization of 10010010011111

1.0010010011111 X 2¹³

Bias for eight bit EXPONENT =127

Actual Exponent= bias+13= 127+13=140

binary value of  140=10001100

sign bit S will be set to 0 (positive decimal value)

Mentissa is given by 0010010011111

Conclusion

32 bit single precision IEEE binary floating point given by following

S(sign)=1bit	E(exponent)=8bits	M(mantisa=23bits)
0	10001100	00100100111110000000000

Hexadecimal format

for 0100-0110-0001-0010-0111-1100-0000-0000 is  46127C00