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Computer Science

Convert the following binary numbers to decimal :

(a) 1100

(b) 10010101

(c) 11011100

Number System

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Answer

(a) 1100

Binary
No
PowerValueResult
0 (LSB)2010x1=0
02120x2=0
12241x4=4
1 (MSB)2381x8=8

Equivalent decimal number = 4 + 8 = 12

Therefore, (1100)2 = (12)10

(b) 10010101

Binary
No
PowerValueResult
1 (LSB)2011x1=1
02120x2=0
12241x4=4
02380x8=0
124161x16=16
025320x32=0
026640x64=0
1 (MSB)271281x128=128

Equivalent decimal number = 1 + 4 + 16 + 128 = 149

Therefore, (10010101)2 = (149)10

(c) 11011100

Binary
No
PowerValueResult
0 (LSB)2010x1=0
02120x2=0
12241x4=4
12381x8=8
124161x16=16
025320x32=0
126641x64=64
1 (MSB)271281x128=128

Equivalent decimal number = 4 + 8 + 16 + 64 + 128 = 220

Therefore, (11011100)2 = (220)10

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