MC0062 – Digital Systems, Computer Organization Q1. Convert the following binary numbers to decimal

a. 11.001 (2)

b. 1100 (2)

c. 1111 (2)

d. 1011.101 (2)

e. 0.1101 (2)

Ans:

a.    11.001 ₍₂₎

= 1×2¹ + 1×2⁰ + 0×2^-1 + 0×2^-2 + 1×2^-3

= 2 + 1 + 0 + 0 + 0.125

= 3.125

b.    1100 ₍₂₎

= 1×2³ + 1×2² + 0×2¹ + 0×2⁰

= 8+4+0+0

= 12

c.    1111 ₍₂₎

= 1×2³ + 1×2² + 1×2¹ + 1×2⁰

= 8 + 4 + 2 + 1

= 15

d.    1011.101 ₍₂₎

= 1×2³ + 0×2² + 1×2¹ + 1×2⁰ + 1×2^-1 + 0×2^-2 + 1×2^-3

= 8 + 0 + 2 + 1 + 0.5 + 0 + 0.125

= 11.625

e. 0.1101 (2)

= 1×2^-1 + 1×2^-2 + 0×2^-3 + 1×2^-4

= 0.5 + 0.25 + 0 + 0.0625

= 0.8125