Decode the following bit patterns using the floating-point format discussed in the text:
a. 01001010
b. 01101101
c. 00111001
d. 11011100
e. 10101011

The sign is stored in bit 8. The exponent can be computed from bits 5-7 by subtracting 3. The mantissa (also known as significant or fraction) is stored in bits 1-4. An invisible leading bit (i.e. it is not actually stored) with value 1.0 is placed in front, then bit 4 has a value of 1/2, bit 3 has value 1/4, bit 2 has value 1/8, and bit 1 has value 1/16.

a. 0 101 1001

sign: 0 (+ve number.)

exp: 101 = 5-3 = 2.

mant: 1.1001.

Therefore: 1.1001 * 2² = 110.01₂ = 2²+2¹+2^-2 = 6.25.

b. 1 100 1000

sign: 1 (-ve number.)

exp: 100 = 4-3 = 1.

mant: 1.1000.

Therefore: 1.1000 * 2¹ = 11.000₂ = 2¹+2⁰ = -3.

c. 1 010 1100

sign: 1 (-ve number.)

exp: 010 = 2-3 = -1.

mant: 1.1100.

Therefore: 1.1100 * 2^-1 = 0.11100₂ = 2^-1+2^-2+2^-3 = -0.875.

d. 0 011 1001

sign: 0 (+ve number.)

exp: 011 = 3-3 = 0.

mant: 1.1001.

Therefore: 1.1001 * 2⁰ = 1.1001₂ = 20+2^-1+2^-4 = 1.5625.