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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

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