Question

1. Write the single-precision Representation for the following decimal number. (-0.625) or -5/8. Final Results must be in HEX. SHOW WORK PLEASE.

2. Given Hexadecimal 0x3F300000, convert it to decimal number if it is a single precision floating point number. SHOW WORK PLEASE.

Answer 1

Single precision format consists of 32 bits.

1 bit allocates for sign

8 bits for exponent.

23 bits for mantissa.

Sign (1 bits)

Exponent (8 bits)

Mantissa (23 bits)

The decimal number = (-1)^s*(1.M)*2^E-127.

Where s is sign, M is mantissa, E is exponent.

1.

Givendecimal number = 0.625.

Convert decimal to binary = 0.101

Write it in single precision format = (1.01)*2^-1

E-127 = -1 =====> E= -1+127 = 126.

Sign s= 0.

Exponent E = 126 = 01111110

Mantissa M = 01000000000000000000000.

0

01111110

01000000000000000000000

HEX format = 0x3F200000.

2.

Given Hexadecimal= 0x3F300000.

Convert into single precision format.

0

01111110

01100000000000000000000

Sign =0.

Exponent E=126.

Mantissa M =  01100000000000000000000.

Decimal number of the single precision format

(-1)⁰*(1.01100000000000000000000)*2^126-127

(1.01100000000000000000000)*2^-1

0.101100000000000000000000

0.6875