Answer to Question #287647 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.

Answer :You first Multiply each digit of the binary number by corresponding power of two

1.1101001=1*2power 5+1*2power5+0*2power4+1*2power3+0*2power2+0*2power1+1*2power0

=1*64+1*32=0*16+1*8+0*4+0*2+1*1=64+32+0+8+0+0+1

Total is 105

So 105 is the decimal number of the binary 1101001

 Answer=105 base 10

2. 10001.1101

1=1*2power4=16

0=0*2power3=0

0=0*2power2=0

0=0*2power1=0

1=0*2power0=1

=17

.1101

1*2power-1+1*2power-2+0*2power-3+1*2power-4=0.5+0.25+0+0.0625

=0.8125

Decimal number of 10001.1101=17.8125 base 10

3. 101110

1=1*2power5=32

0=0*2power4=0

1=1*2power3=8

1=1*2power2=4

1=1*2power1=2

0=0*2power0=0

=46 base 10

4. 101010.1111

1=1*32=32

0=0*16=0

1=1*8=8

0=0*4=0

1=1*2=2

0=0*1=0

=42

.1111

.1=1*0.5

.1=1*0.25

1=1*0.125

1=1*0.0625

=0.9375

Decimal number of 101010.1111 is 42.9375 base 10

5. 111001

1=1*32=32

1=1*16=16

1=1*8=8

0=0*4=0

0=0*2=0

1=1*1=1

Decimal number of 111001 =57 base 10

Convert the following decimal numbers to binary.

1.     76

In this case we use binary numbers (powers of twos)

128,64, 32,16,8,4,2,1

76 is like adding 64+8+2

64=1, 32=0,16=0,8=1.4=0,2=1

76=100101base 2

2.     119=

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

119=1110111 base 2

3. 1032

1032 its binary is by dividing by two and taking the remainder as answer

1032/2=516 rem. 0

516/2=258 rem 0

258/2=129 rem.0

129/2=64 rem. 1

64/2=32 rem.0

32/2=16 rem.0

16/2=8 rem .0

8/2=4 rem.0

4/2=2 rem.0

2/2=1rem.0

½=0 rem 1

Binary of 1032 is 00010000001

3.     1010

Binary

1010/2=505 rem 0

505/2=252 rem 1

252/2=126 rem. 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

½=0 rem 1

Its binary is 0100111111

5. 242

Binary

242/2=121 rem .0

121/2=60 rem 1

60/2=30 rem 0

30/2=15rem 1

15/2=7 rem.1

7/2=3 rem.1

3/2=1 rem. 1

½=0 rem 1

Binary of 242 is 01011111