Question

Perform the following using 10-bit floating point notation having the format SEEEMMMMMM:

a. Decode 1101110110 to decimal integer and/or fraction.

b. Decode 0001100000 to decimal integer and/or fraction.

c. Encode: -5/32

d. Encode: +6 and 5/8

If someone could send the answer with explanations please do. It will be greatly appreciated.

Answer 1

1=> sign is negative

101 => Exponent = 5-3 = 2

110110 => Mantissa

Decimal: - 1.110110 * 2^2 = -111.0110 = -7.375

0=> sign is positive

001 => Exponent = 1-3 = -2

100000 => Mantissa

Decimal: 1.100000 * 2^-2 = 0.011 = 0.75

-5/32= -1/32 - 1/8 = -0.00001 -0.00100 =-0.00101

= -1.01* 2^-3

= 1000010000

6= 110 = 1.10 * 2^2 = 0101100000

5/8 = 1/8+1/2 = 0.100+0.001 = 0.101

= 1.01 * 2^-1

= 0010010000

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