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CBSE Class 11 Computer Science Question 6 of 91

Data Representation — Question 6

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Question 6

Convert the following binary numbers to decimal and hexadecimal:

(a) 1010

(b) 111010

(c) 101011111

(d) 1100

(e) 10010101

(f) 11011100

Answer

(a) 1010

Converting to decimal:

Binary
No		PowerValueResult
0 (LSB)2010x1=0
12121x2=2
02240x4=0
1 (MSB)2381x8=8

Equivalent decimal number = 8 + 2 = 10

Therefore, (1010)2 = (10)10

Converting to hexadecimal:

Grouping in bits of 4:

1010undefined\underlinesegment{1010}

Binary
Number		Equivalent
Hexadecimal
1010A (10)

Therefore, (1010)2 = (A)16

(b) 111010

Converting to decimal:

Binary
No		PowerValueResult
0 (LSB)2010x1=0
12121x2=2
02240x4=0
12381x8=8
124161x16=16
1 (MSB)25321x32=32

Equivalent decimal number = 32 + 16 + 8 + 2 = 58

Therefore, (111010)2 = (58)10

Converting to hexadecimal:

Grouping in bits of 4:

0011undefined1010undefined\underlinesegment{0011} \quad \underlinesegment{1010}

Binary
Number		Equivalent
Hexadecimal
1010A (10)
00113

Therefore, (111010)2 = (3A)16

(c) 101011111

Converting to decimal:

Binary
No		PowerValueResult
1 (LSB)2011x1=1
12121x2=2
12241x4=4
12381x8=8
124161x16=16
025320x32=0
126641x64=64
0271280x128=0
1 (MSB)282561x256=256

Equivalent decimal number = 256 + 64 + 16 + 8 + 4 + 2 + 1 = 351

Therefore, (101011111)2 = (351)10

Converting to hexadecimal:

Grouping in bits of 4:

0001undefined0101undefined1111undefined\underlinesegment{0001} \quad \underlinesegment{0101} \quad \underlinesegment{1111}

Binary
Number		Equivalent
Hexadecimal
1111F (15)
01015
00011

Therefore, (101011111)2 = (15F)16

(d) 1100

Converting to decimal:

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

Equivalent decimal number = 8 + 4 = 12

Therefore, (1100)2 = (12)10

Converting to hexadecimal:

Grouping in bits of 4:

1100undefined\underlinesegment{1100}

Binary
Number		Equivalent
Hexadecimal
1100C (12)

Therefore, (1100)2 = (C)16

(e) 10010101

Converting to decimal:

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

Converting to hexadecimal:

Grouping in bits of 4:

1001undefined0101undefined\underlinesegment{1001} \quad \underlinesegment{0101}

Binary
Number		Equivalent
Hexadecimal
01015
10019

Therefore, (101011111)2 = (95)16

(f) 11011100

Converting to decimal:

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

Converting to hexadecimal:

Grouping in bits of 4:

1101undefined1100undefined\underlinesegment{1101} \quad \underlinesegment{1100}

Binary
Number		Equivalent
Hexadecimal
1100C (12)
1101D (13)

Therefore, (11011100)2 = (DC)16