Question

Represent the decimal number +105.25 as a sign (S), mantissa (M), and exponent (E)

Answer 1

Single precision (Sign(s),Mantissa(M),and Exponent(E)):

• Sign of Mantissa (S)( 0 represents positive 1 represents negative) (1bit)
• Exponent(E) (127 actual for Single precision) (8 bits)
• Mantissa(M) (23 bits)

Step 1: Write binary of a decimal mumber

(105.25)₁₀ =(1101001.01)₂

Step 2: Write binary number in a power of 2

1.10100101 * 2⁶ (2⁶ because we shift decimal by 6)

(10100101) is calles a normalised mantisa

Sign bit is 0 because number is positive.

Step 3: add 6(power of 2) in actual exponent (127)

127+6=133

Step 4: Conver 133 into binary

(133)₁₀ =(10000101)₂

Step 5 : make 23 bit Normalized mantisa by adding extra 0's

  10100101000000000000000

Step 6 : Write Sign, Exponent and mantisa in their format, Format is:

Sign(1bit)

Exponent(8bits)

Mantisa(23 bits)

(0  10000101   10100101000000000000000)

So,

(+105.25) as a sign (S), mantissa (M), and exponent (E) is (0  10000101   10100101000000000000000)

0  10000101   10100101000000000000000(Answer)