Question

Convert the following numbers from binary 2 to base 10:
1. 11 =
2. 100 =
3. 1001=
4. 1101=
5. 11101=

Convert the following numbers from binary 10 to base 2:
1. 28
2. 17
3. 81
4. 64
5. 45
Please sharp!

Answer 1

Given : few Binary & Decimal Numbers

To find : Convert Binary into decimals & decimals into Binary

Solution:

Binary are the number consisting of 0 & 1

Base 10 are numbers having digits  0 to 9

11₂  =  1 * 2¹  + 1 * 2⁰   =  2 +  1  = 3

100₂ = 1 * 2²  + 0 * 2¹  + 0 * 2⁰ = 4 + 0 + 0  = 4

1001₂ =  1 * 2³ +  0 * 2²  + 0 * 2¹  + 1 * 2⁰ =  8 + 0 + 0  + 1 = 9

1101₂ =  1 * 2³ +  1 * 2²  + 0 * 2¹  + 1 * 2⁰ =  8 + 4 + 0  + 1 = 13

11101₂ =  1 * 2⁴ + 1 * 2³ +  1 * 2²  + 0 * 2¹  + 1 * 2⁰ =  16 + 8 + 4 + 0  + 1 = 29

From Base 10  to Binary

     28  

2    14   0

2     7    0

2     3     1

2      1      1

2      0      1

28₁₀  = ( 11100)₂

Similarly

 17  =  (10001)₂

81  = ( 1010001)₂

64   = (1000000)₂

45 = ( 101101)₂

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Answer 2

Binary ⇄ decimal conversion

Step-by-step explanation:

Binary to decimal conversion:

1. 11 = 2 + 1 = 3

2. 100 = 4 + 0 + 0 = 4

3. 1001= 8 + 0 + 0 + 1 = 9

4. 1101= 8 + 4 + 0 + 1 = 13

5. 11101= 16 + 8 + 4 + 0 + 1 = 29

Decimal to binary conversion:

1. 28 = 11100

2. 17 = 10001

3. 81 = 1010001

4. 64 = 1000000

5. 45 = 101101

Please see the attached picture for the workings of an example for each conversion.