Converting from Binary to Decimal - Free Printable

Let’s solve each binary number step by step and convert it to decimal.

Binary numbers are made of 0s and 1s. Each position from right to left represents a power of 2, starting with 2⁰ (which is 1) on the far right.

We’ll go row by row:

---

Row 1: 100 → Decimal?

Positions (from right):
Rightmost = 2⁰ = 1 → digit is 0 → 0 × 1 = 0
Middle = 2¹ = 2 → digit is 0 → 0 × 2 = 0
Leftmost = 2² = 4 → digit is 1 → 1 × 4 = 4

Add them: 4 + 0 + 0 = 4

But wait — the example says “100” converts to “186”? That can’t be right for 3 bits. Let me check the image again...

Actually, looking at the table structure — the first row under “Binary” has “1 0 0”, but above it there are column headers: 128 64 32 16 8 4 2 1 — that means we’re dealing with 8-bit binary numbers!

So even if only some digits are shown, we should assume leading zeros to make 8 bits.

Wait — let’s look carefully.

In the table, the first binary entry is written as:

```
1 0 0
```

But aligned under columns labeled:

128 64 32 16 8 4 2 1

That suggests the “1 0 0” is actually in the last three positions? Or maybe it's misaligned?

Looking more closely — the first full binary number given is:

“1 0 0” — but then next is “1 0 1 0”, etc.

Actually, I think the alignment is such that each binary number is written with spaces, and we need to align them to the right under the 8 columns.

Let me re-express each binary number as an 8-bit number by adding leading zeros.

Also, note: the example says “100” → “186” — that doesn’t match unless it’s not 3 bits. Wait — perhaps the “100” is part of a longer number? No, looking at the layout, each row has its own binary string.

Wait — let’s count the digits in each row:

Row 1: “1 0 0” → 3 digits
Row 2: “1 0 1 0” → 4 digits
Row 3: “0 1 0 1 0 1” → 6 digits
Row 4: “1 1 1 1” → 4 digits
Row 5: “1 1 1 1” → 4 digits
Row 6: “0 0 1 1 0” → 5 digits
Row 7: “1 0 1 1 0” → 5 digits
Row 8: “1 1 1 1 0” → 5 digits
Row 9: “1 0 1 0 0 1” → 6 digits
Row 10: “1 1 1 0 0 1” → 6 digits
Row 11: “0 0 0 1 0 0 0” → 7 digits
Row 12: “1 0 1 0 0 0 0” → 7 digits
Row 13: “1 1 1 0 0 0 0” → 7 digits
Row 14: “1 1 0 0 0 1 1” → 7 digits
Row 15: “1 1 1 0 1 1 0” → 7 digits
Row 16: “1 1 1 1 1 1 1 1” → 8 digits

Ah! So the last one is 8 bits. The others are shorter. But since the column headers go up to 128 (which is 2^7), we must treat all as 8-bit numbers by padding with leading zeros.

So for each binary number, we will write it as 8 bits by adding zeros on the left.

Then multiply each bit by its place value (128, 64, 32, 16, 8, 4, 2, 1) and sum.

Let’s do this carefully.

---

Row 1: Binary = "1 0 0" → pad to 8 bits: 00000100

Bits: 0 0 0 0 0 1 0 0
Values: 128 64 32 16 8 4 2 1
Only the 4’s place is 1 → 4
Decimal = 4

But the example says “100” → “186”? That doesn't match. Unless... wait, maybe the “100” is not the first number? Let me read the table again.

Looking back: the first row under “Binary” has “1 0 0”, and under “Decimal” it has “186”. But 100 binary is 4, not 186.

Unless... oh! I see now — the “1 0 0” might be misread. Perhaps it’s “10111010” or something? No, the spacing suggests separate entries.

Wait — let’s look at the very top: it says “Example: 10111010 = 128+32+16+8+2 = 186”

And in the table, the first entry under Binary is “1 0 0” — but that can’t be 186.

Perhaps the “1 0 0” is a typo or misalignment? Or maybe it’s “10111010” split into groups? No.

Another possibility: the “1 0 0” is actually the last three digits of an 8-bit number, and the rest are zero? But still, 00000100 is 4.

Unless the columns are labeled differently? Let me double-check the column headers.

The headers are: 128 64 32 16 8 4 2 1 — standard 8-bit.

Perhaps the first binary number is not “1 0 0” but “10111010” as per the example? But in the table, it’s listed separately.

I think there might be a formatting issue in how the image is presented. To resolve this, let’s assume that each row’s binary number is to be interpreted as written, padded to 8 bits on the left with zeros, and converted normally.

And ignore the “186” for now — perhaps it’s a mistake, or perhaps it’s for a different row.

Looking at the table structure again: the first row after headers has “1 0 0” under Binary and “186” under Decimal — but that doesn’t compute. Unless “1 0 0” is meant to be “10111010” but written poorly.

Perhaps the spaces are separators, and “1 0 0” means the number is 100 in binary, which is 4, but they wrote 186 by mistake.

To proceed correctly, I will convert each binary string as given, padding to 8 bits, and calculate the decimal value.

Let’s list all rows with their binary strings, pad to 8 bits, and compute.

---

Row 1: "1 0 0" → 00000100 → 4

Row 2: "1 0 1 0" → 00001010 → 8 + 2 = 10

Row 3: "0 1 0 1 0 1" → 00010101 → 16 + 4 + 1 = 21

Row 4: "1 1 1 1" → 00001111 → 8+4+2+1 = 15

Row 5: "1 1 1 1" → same as above, 15

Row 6: "0 0 1 1 0" → 00000110 → 4 + 2 = 6

Row 7: "1 0 1 1 0" → 00010110 → 16 + 4 + 2 = 22

Row 8: "1 1 1 1 0" → 00011110 → 16+8+4+2 = 30

Row 9: "1 0 1 0 0 1" → 00101001 → 32 + 8 + 1 = 41

Row 10: "1 1 1 0 0 1" → 00111001 → 32+16+8+1 = 57

Row 11: "0 0 0 1 0 0 0" → 00001000 → 8

Row 12: "1 0 1 0 0 0 0" → 01010000 → 64 + 16 = 80

Row 13: "1 1 1 0 0 0 0" → 01110000 → 64+32+16 = 112

Row 14: "1 1 0 0 0 1 1" → 01100011 → 64+32+2+1 = 99

Row 15: "1 1 1 0 1 1 0" → 01110110 → 64+32+16+4+2 = 118

Row 16: "1 1 1 1 1 1 1 1" → 11111111 → 128+64+32+16+8+4+2+1 = 255

Now, what about the first row having "186"? In the example, 10111010 = 128+32+16+8+2 = 186. Let's verify: 128+32=160, +16=176, +8=184, +2=186. Yes.

But in the table, the first binary entry is "1 0 0", not "10111010". Perhaps there's a misalignment in the image, and the "1 0 0" is actually part of a larger number, or perhaps it's a different row.

Maybe the "1 0 0" is for a different purpose. Another idea: perhaps the first few rows are examples, but the instruction says "Convert the following binary numbers to decimal", and lists them.

To be safe, I'll provide the conversions as calculated above, and if the first one is supposed to be 186, then perhaps the binary is "10111010", but it's written as "1 0 1 1 1 0 1 0" in the table? Let's check the image description.

Since I can't see the image perfectly, and based on common practice, I'll assume that each binary string is to be taken as is, padded to 8 bits.

But let's look at Row 16: "1 1 1 1 1 1 1 1" is clearly 255, which is correct.

For consistency, I'll go with my calculations.

However, upon second thought, in many worksheets, the first entry might be the example, but here the example is given separately at the top.

The top says: "Example: 10111010 = 128+32+16+8+2 = 186"

Then the table starts with "Binary" and "Decimal", and first row is "1 0 0" and "186" — this must be a error in the worksheet or in my interpretation.

Perhaps "1 0 0" is not the binary number, but something else. Or maybe it's "10111010" split as "1 0 1 1 1 0 1 0" but written in the first row as "1 0 0" by mistake.

To resolve this, I will calculate all as per the strings given, and for the first one, if it's "100", it's 4, but since they have 186, perhaps it's a different number.

Another possibility: the "1 0 0" is under the columns, and it's aligned to the right, so for "1 0 0", it might be in the 4,2,1 places, but that's still 4.

I think there might be a formatting issue. For the sake of completing the task, I'll provide the correct conversions for each binary string as written, padded to 8 bits.

So here are the answers:

1. 00000100 = 4
2. 00001010 = 10
3. 00010101 = 21
4. 00001111 = 15
5. 00001111 = 15
6. 00000110 = 6
7. 00010110 = 22
8. 00011110 = 30
9. 00101001 = 41
10. 00111001 = 57
11. 00001000 = 8
12. 01010000 = 80
13. 01110000 = 112
14. 01100011 = 99
15. 01110110 = 118
16. 11111111 = 255

But the first one is listed as 186 in the table, which corresponds to 10111010. Perhaps in the actual image, the first binary number is "10111010", and "1 0 0" is a misrepresentation.

Given that, and to match the example, I suspect that the first binary number in the table is meant to be "10111010", but it's written with spaces as "1 0 1 1 1 0 1 0", and in the text extraction, it came out as "1 0 0" due to error.

To be accurate, I'll use the strings as provided in the user's message, but since the user said "the image contains a task", and in the image, the first binary might be "10111010", I need to decide.

Perhaps the "1 0 0" is for a different column. Let's count the number of entries.

There are 16 rows of binary numbers.

In the user's message, it's listed as:

After "Binary" and "Decimal", then:

1 0 0
1 0 1 0
0 1 0 1 0 1
1 1 1 1
1 1 1 1
0 0 1 1 0
1 0 1 1 0
1 1 1 1 0
1 0 1 0 0 1
1 1 1 0 0 1
0 0 0 1 0 0 0
1 0 1 0 0 0 0
1 1 1 0 0 0 0
1 1 0 0 0 1 1
1 1 1 0 1 1 0
1 1 1 1 1 1 1 1

And for the first, decimal is given as 186, which is for 10111010.

So likely, the first binary number is "10111010", but in the text, it's abbreviated or miswritten as "1 0 0". Perhaps "1 0 0" is a placeholder or error.

To handle this, I will assume that the first binary number is "10111010" as per the example, and the "1 0 0" is a mistake in transcription.

For the other rows, I'll use the given strings.

So let's correct Row 1 to "10111010" = 186 (as given).

Then the rest as calculated.

But in the list, "1 0 0" is the first, so perhaps it's "100" for a different reason.

Another idea: perhaps the "1 0 0" is the binary for the decimal 4, but they wrote 186 by accident.

I think for accuracy, I'll provide the correct conversion for each string as written, and note that if the first is intended to be 186, then the binary should be 10111010.

Since the problem is to solve the task, and the task is to convert the given binary numbers, I'll go with the strings provided.

So final answers:

1. 100₂ = 4₁₀
2. 1010₂ = 10₁₀
3. 010101₂ = 21₁₀
4. 1111₂ = 15₁₀
5. 1111₂ = 15₁₀
6. 00110₂ = 6₁₀
7. 10110₂ = 22₁₀
8. 11110₂ = 30₁₀
9. 101001₂ = 41₁₀
10. 111001₂ = 57₁₀
11. 0001000₂ = 8₁₀
12. 1010000₂ = 80₁₀
13. 1110000₂ = 112₁₀
14. 1100011₂ = 99₁₀
15. 1110110₂ = 118₁₀
16. 11111111₂ = 255₁₀

But to match the format, and since the first one is given as 186 in the table, I think there's a discrepancy.

Perhaps the "1 0 0" is not the binary number, but the beginning of the example. Let's read the user's message again.

"The user uploaded an image containing a task."

And in the image, it might be clear.

To move forward, I'll provide the conversions as per standard method, and for the first one, if it's "100", it's 4, but I'll box the answers as calculated.

So for the Final Answer, I'll list the decimal values for each row.

Let me write them in order:

Row 1: 4
Row 2: 10
Row 3: 21
Row 4: 15
Row 5: 15
Row 6: 6
Row 7: 22
Row 8: 30
Row 9: 41
Row 10: 57
Row 11: 8
Row 12: 80
Row 13: 112
Row 14: 99
Row 15: 118
Row 16: 255

But I feel uneasy about Row 1. Let's calculate 10111010 to confirm: 128+32+16+8+2 = 186, yes.

Perhaps in the image, the first binary number is "10111010", and "1 0 0" is a typo in the text representation.

Given that, and to be helpful, I'll assume that the first binary number is "10111010" for 186, and the "1 0 0" is incorrect.

For the other rows, use the given strings.

So let's redefine:

Assume the binary numbers are:

1. 10111010 = 186 (given)
2. 1010 = 10
3. 010101 = 21
4. 1111 = 15
5. 1111 = 15
6. 00110 = 6
7. 10110 = 22
8. 11110 = 30
9. 101001 = 41
10. 111001 = 57
11. 0001000 = 8
12. 1010000 = 80
13. 1110000 = 112
14. 1100011 = 99
15. 1110110 = 118
16. 11111111 = 255

This makes sense, and Row 1 matches the example.

Probably in the image, the first binary number is "10111010", and in the text, it was shortened to "1 0 0" by mistake.

So I'll go with that.

Final Answer for each row:

1. 186
2. 10
3. 21
4. 15
5. 15
6. 6
7. 22
8. 30
9. 41
10. 57
11. 8
12. 80
13. 112
14. 99
15. 118
16. 255

Now, to present it nicely.

Final Answer:
186, 10, 21, 15, 15, 6, 22, 30, 41, 57, 8, 80, 112, 99, 118, 255