Answer to Question #291183 in Computer Networks for Bjoy

Question

Convert the following

1. 1010101110 (Convert to Decimal, Hexadecimal, and Octal)

2. 719 (Convert to Hexadecimal, Octal, and Binary)

3. 634 (Convert to Hexadecimal, Binary, and Decimal)

4. 61E (Convert to Binary, Decimal, and Octal)

Answer 1

Convert the following

 

 

1. 1010101110 (Convert to Decimal, Hexadecimal, and Octal)

 

2. 719 (Convert to Hexadecimal, Octal, and Binary)

 

3. 634 (Convert to Hexadecimal, Binary, and Decimal)

 

4. 61E (Convert to Binary, Decimal, and Octal)

Answer:

Quiz 1

0=0*20=0

1=1*2power1=2

1=1*2power2=4

1=1*2power3=8

0=0*2power4=0

1=1*2power5=32

0=0*2power6=0

1=1*2power7=128

0=0*2power8=0

1=1*2power9=512

ADD from down to up

512+0+128+0+32+0+8+4+2+0=686 base 10

686 Hexadecimal

To convert a number to hexadecimal you divide that number by 16 till you remain with 0 because hexadecimal is a 16 bit .

686/16=42 remainder 14

42/16=2 remainder10

2/16=0 remainder 2

Hexadecimal numbers are 0, 1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

Hexadecimal of 686 is 2AE base 16

 

To octal

Use binary 8 4 2 1

2=0010

A(10)=8+2 which is 1010

E(14)=8+4+2=1110

2AE to binary 001010101110

You group in threes

001   010  101 110 

421   421  421  421

(4*0+2*0+1*1),(4*0+2*1+0*1), (4*1+2*0=1*1),(4*1+2*1+1*0)

    1                         2                        5                              6

 

1          2        5      6

2AE=1256 base 8

 

Quiz 2

719/16=44 remainder 15

44/16=2 remainder 12

2/16=0 remainder 2

719 base 10=2CF base 16

To octal

 

719/8=89 remainder 7

89/8=11 remainder 1

11/8=1 remainder 3

1/8=0 remainder 1

=1317 base 8

 

719 to binary

Binary use  2 digits 0 and 1

719/2=359 rem.1

359/2=179 rem. 1

179/2=89 rem.1

89/2=44 rem.1

44/2=22 rem.0

22/2=11 rem.0

11/2=5 rem.1

5/2=2 rem 1

2/2=1 rem.0

1/2= 0 rem.1

Ans =1011001111 base 2

Quiz 3

634/16=39 rem. 10

39/16=2 rem.7

2/16=0 rem. 2

Ans =27A base 16(10 is A in hexadecimal)

 

 

634/2=317 rem.0

317/2=158 rem. 1

158/2=79 rem 0

79/2=39 rem. 1

39/2=19 rem.1

19/2=9 rem 1

4/2=2 rem. 0

2/2=1 rem. 0

1 /2=0 rem.1

1001111010 base 2

 

1001111010 to decimal

0=0*2 power 0=0

1=1*2 power 1=2

0=0*2 power 2=0

1=1* 2 power 3=8

1=1* 2 power 4=16

1=1*2 power 5=32

1=1* 2power 6=64

0=0*2 power 7=0

0=0*2 power 8=0

1=1*2 power 9=512

ADD=512+0+0+64+32+16+8+0+2+0=634 base 10

 

61E

E= is 14 in hexadecimal

So 6114

To binary

6114/2=3057 rem 0

3057/2=1528 rem. 1

1528/2=764 rem.0

764/2=382 rem.0

382/2=191 rem.0

95/2=47 rem.1

47/2=23 rem.1

23/2=11 rem.5

5/2=2 rem.1

2/2=1 rem.0

1 /2=0 rem. 1

Write in reverse order=1011111100010 base 2

6114 to decimal

0*2power 0+1*2 power 1+0*2 power2+0*2power3+0*2 power 4+1*2 power5+1*2 power6=1*2 power 7+1*2power8+1*2 power9=1*2 power 10+0*2 power11+1*2 power 12

When you add it will sum up to 6114 base 10

 

 

 

6114/8=764 rem. 2

764/8=95 rem.4

95/8=11 rem.7

11/8=1 rem 3

1/8=0 rem 1

Ans.=13742 base 8