Converting Binary to Decimal worksheet with ten exercises for practice.

To convert a binary number to a decimal number, we look at the position of each digit (bit). Each position represents a power of 2, starting from the rightmost digit which is $2^0$ (value 1). As we move left, the values double: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, etc.

We only add up the values for the positions where there is a 1. If there is a 0, we skip that value.

Here is the step-by-step solution for each problem:

1. Binary = 1001
* Positions (from right): 1, 0, 0, 1
* Values: $1 \times 1$, $0 \times 2$, $0 \times 4$, $1 \times 8$
* Calculation: $8 + 1 = 9$
* Decimal = 9

2. Binary = 100000
* Positions: 1, 0, 0, 0, 0, 0
* The '1' is in the 6th position from the right ($2^5$).
* Value: $32$
* Decimal = 32

3. Binary = 1100101101
* Let's align the bits with their values (starting from right):
* 1 ($1$)
* 0 ($2$)
* 1 ($4$)
* 1 ($8$)
* 0 ($16$)
* 1 ($32$)
* 0 ($64$)
* 0 ($128$)
* 1 ($256$)
* 1 ($512$)
* Add the values where there is a 1: $512 + 256 + 32 + 8 + 4 + 1$
* $512 + 256 = 768$
* $768 + 32 = 800$
* $800 + 8 = 808$
* $808 + 4 = 812$
* $812 + 1 = 813$
* Decimal = 813

4. Binary = 100001000
* Align bits with values:
* 0 ($1$)
* 0 ($2$)
* 0 ($4$)
* 1 ($8$)
* 0 ($16$)
* 0 ($32$)
* 0 ($64$)
* 0 ($128$)
* 1 ($256$)
* Add the values: $256 + 8$
* Decimal = 264

5. Binary = 10101001
* Align bits with values:
* 1 ($1$)
* 0 ($2$)
* 0 ($4$)
* 1 ($8$)
* 0 ($16$)
* 1 ($32$)
* 0 ($64$)
* 1 ($128$)
* Add the values: $128 + 32 + 8 + 1$
* $128 + 32 = 160$
* $160 + 8 = 168$
* $168 + 1 = 169$
* Decimal = 169

6. Binary = 1010000100
* Align bits with values:
* 0 ($1$)
* 0 ($2$)
* 1 ($4$)
* 0 ($8$)
* 0 ($16$)
* 0 ($32$)
* 0 ($64$)
* 1 ($128$)
* 0 ($256$)
* 1 ($512$)
* Add the values: $512 + 128 + 4$
* $512 + 128 = 640$
* $640 + 4 = 644$
* Decimal = 644

7. Binary = 1011010111
* Align bits with values:
* 1 ($1$)
* 1 ($2$)
* 1 ($4$)
* 0 ($8$)
* 1 ($16$)
* 0 ($32$)
* 1 ($64$)
* 1 ($128$)
* 0 ($256$)
* 1 ($512$)
* Add the values: $512 + 128 + 64 + 16 + 4 + 2 + 1$
* $512 + 128 = 640$
* $640 + 64 = 704$
* $704 + 16 = 720$
* $720 + 4 = 724$
* $724 + 2 = 726$
* $726 + 1 = 727$
* Decimal = 727

8. Binary = 1010101111
* Align bits with values:
* 1 ($1$)
* 1 ($2$)
* 1 ($4$)
* 1 ($8$)
* 0 ($16$)
* 1 ($32$)
* 0 ($64$)
* 1 ($128$)
* 0 ($256$)
* 1 ($512$)
* Add the values: $512 + 128 + 32 + 8 + 4 + 2 + 1$
* $512 + 128 = 640$
* $640 + 32 = 672$
* $672 + 8 = 680$
* $680 + 4 = 684$
* $684 + 2 = 686$
* $686 + 1 = 687$
* Decimal = 687

9. Binary = 110111110100
* Align bits with values:
* 0 ($1$)
* 0 ($2$)
* 1 ($4$)
* 0 ($8$)
* 1 ($16$)
* 1 ($32$)
* 1 ($64$)
* 1 ($128$)
* 1 ($256$)
* 0 ($512$)
* 1 ($1024$)
* 1 ($2048$)
* Add the values: $2048 + 1024 + 256 + 128 + 64 + 32 + 16 + 4$
* $2048 + 1024 = 3072$
* $256 + 128 = 384$
* $64 + 32 + 16 = 112$
* $3072 + 384 = 3456$
* $3456 + 112 = 3568$
* $3568 + 4 = 3572$
* Decimal = 3572

10. Binary = 110110101111
* Align bits with values:
* 1 ($1$)
* 1 ($2$)
* 1 ($4$)
* 1 ($8$)
* 0 ($16$)
* 1 ($32$)
* 0 ($64$)
* 1 ($128$)
* 1 ($256$)
* 0 ($512$)
* 1 ($1024$)
* 1 ($2048$)
* Add the values: $2048 + 1024 + 256 + 128 + 32 + 8 + 4 + 2 + 1$
* $2048 + 1024 = 3072$
* $256 + 128 = 384$
* $32 + 8 + 4 + 2 + 1 = 47$
* $3072 + 384 = 3456$
* $3456 + 47 = 3503$
* Decimal = 3503

Final Answer:
1. Decimal = 9
2. Decimal = 32
3. Decimal = 813
4. Decimal = 264
5. Decimal = 169
6. Decimal = 644
7. Decimal = 727
8. Decimal = 687
9. Decimal = 3572
10. Decimal = 3503