Answer to Question #287519 in Computer Networks for Bjoy

Question

Convert the following to binary numbers to decimals using the long method.

1. 1101001

2. 10001.1101

3. 101110

4. 101010.1111

5. 111001

Convert the following decimal numbers to binary.

1. 76

2. 119

3. 1032

4. 1010

5. 242

Answer 1

Convert the following to binary numbers to decimals using the long method.

1. 1101001

1=2power5=32

1=2power4=16

0=2power3=0

1=2power2=4

0=2power1=0

1=2power 0 =1

Add 0+2+4+0+16+32 =53

Answer is 53 base 10

2. 10001.1101

1=2power4=16

0=2power3=0

0=2power2=0

0=2power1=0

1=2power0=1

Add= 17

.1101=

1=2power-1=0.5

1=2power-2=0.125

0=2power-3=0

1=2power-4=0.0625

=.8125

Answer for 10001.1101 to decimal is 17.8125

3. 101110

1=2power5=32

0=2power4=0

1=2power3=8

1=2power2=4

1=2power1=1

0=2power0=0

Add=1+4+8+32=45

Answer=45base 10

4. 101010.1111

1=2power5=32

0=2power4=0

1=2power3=8

0=2power2=0

1=2 power 1=2

0=2 power 0=0

.1111

1=2power-1=0.5

1=2power-2=0.25

1=2power-3=0.125

1=2power-4=0.0625

Answer of 101010.11111=42.9375 base 10

5. 111001

1=2power5=32

1=2power4=16

1=2power3=8

0=2power2=0

0=2power1=0

1=2power0=1

Add=57

Answer=57 base 10

Convert the following decimal numbers to binary.

1.     76=

binary numbers

powers of two from 0 to 7 respectively are-1,2,4,8,16,32,64,128

we arrange this way128,64,32,16,8,4,2,1

binary of 76 is 64 ,76-64=12,you look for 8,12-8 is 4

64+8+4=76 in binary is 1001100

2. 119

Is 64+32+16+4+2+1

In binary is 1110111

3. 1032

Is divide 1032 by 2 until remainder 1

1032/2=516 rem.0

516/2=258 rem.0

258/2=129rem.0

129/2=64rem.1

32/2=16 rem.0

16/2=8 rem.0

8/2=4rem.0

4/2=2 rem.0

2/2=1rem0

1/2=0rem.1

Answer=Copy remainders upwards=answer is 10000001000 base 2

4. 1010

1010/2=505 rem.0

505/2=252rem.1

252/2=126rem.0

126/2=63 rem 0

63/2=31 rem 1

31/2=15 rem 1

15/2=7 rem 1

7/2=3 rem 1

3/2=1 rem 1

1/2= 0 rem 1

Answer=1111110010 base 2

5. 242

Binary of this number after dividing the number with twos till remaining only with one is

Answer =11110010 base 2