Question

Convert this binary into decimal:

1) (111000)
2) (110011)
3) (111010)
4) (100001)
5) ( 11000)

Explain how the answer come
With the help of image​

Answer 1

hope it helpful

these are the picture may be it would be helpful

I don't know how to convert binary into decimal

Answer 2

Answer:

1. 56

2. 51

3. 58

4. 33

5. 24

Explanation:

$1) \: \: \: 111000 _{(2)} \\ = (1 \times {2}^{5} ) + (1 \times {2}^{4} ) + (1 \times {2}^{3} ) + (0 \times {2}^{2} ) + (0 \times {2}^{1} ) + (0 \times {2}^{0} ) \\ = 32 + 16 + 8 + 0 + 0 + 0 \\ \boxed{ = \underline{ \underline{ \large 56 _{(10)}}}} \\ \\ 2) \: \: \: 110011 _{(2)} \\ = (1 \times {2}^{5} ) + (1 \times {2}^{4} ) + (0 \times {2}^{3} ) + (0 \times {2}^{2} ) + (1 \times {2}^{1} ) + (1 \times {2}^{0} ) \\ = (1 \times 32) + (1 \times 16) + (0 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1) \\ = 32 + 16 + 0 + 0 + 2 + 1 \\ \boxed{ = \underline{ \underline{ \large 51 _{(10)}}}} \\ \\ 3) \: \: \: 111010 _{(2)} \\ = (1 \times {2}^{5} ) + (1 \times {2}^{4} ) + (1 \times {2}^{3} ) + (0 \times {2}^{2} ) + (1 \times {2}^{1} ) + (0 \times {2}^{0} ) \\ = (1 \times 32) + (1 \times 16) + (1 \times 8) + (0 \times 4) + (1 \times 2) + (0 \times 1) \\ = 32 + 16 + 8 + 0 + 2 + 0 \\ \boxed{ = \underline{ \underline{ \large 58 _{(10)}}}} \\ \\ 4) \: \: \: 100001 _{(2)} \\ = (1 \times {2}^{5} ) + (0 \times {2}^{4} ) + (0 \times {2}^{3} ) + (0 \times {2}^{2} ) + (0 \times {2}^{1} ) + (1 \times {2}^{0} ) \\ = (1 \times 32) + (0 \times 16) + (0 \times 8 ) + (0 \times 4) + (0 \times 2) + (1 \times 1) \\ = 32 + 0 + 0 + 0 + 0 + 1 \\ \boxed{ = \underline{ \underline{ \large 33 _{(10)}}}} \\ \\ 5) \: \: \: 11000 _{(2)} \\ = (1 \times {2}^{4} ) + (1 \times {2}^{3} ) + (0 \times {2}^{2} ) + (0 \times {2}^{1} ) + (0 \times {2}^{0} ) \\ = (1 \times 16) + (1 \times 8) + (0 \times 4) + (0 \times 2) + (0 \times 1) \\ = 16 + 8 + 0 + 0 + 0 \\ \boxed{ = \underline{ \underline{ \large 24 _{(10)}}}}$