Worksheet 14 Addition of Hexadecimal Numbers online exercise for ... - Free Printable

Let's solve the hexadecimal addition problems step by step.

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Problem 1: Add $ 4C799_{16} + 56F84_{16} $

First, recall that:
- Hexadecimal digits go from 0–9 and then A–F, where:
- A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

So:
- C = 12
- F = 15

We will add column by column from right to left (like decimal addition), carrying over when the sum exceeds 15.

```
4 C 7 9 9
+ 5 6 F 8 4
-------------------
```

We’ll label columns from right to left as Column 1 to Column 5.

---

#### Column 1 (rightmost): 9 + 4
- 9 + 4 = 13 → 13 in hex is D, no carry.
- But wait! Let’s do it properly:

Wait — actually, let’s write each digit:

```
4 C 7 9 9
+ 5 6 F 8 4
---------------------
```

Start from Column 1 (units place):

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✔ Step-by-step Addition:

#### Column 1: 9 + 4 = 13
- 13 in hex = D
- No carry (since < 16)
→ Write D, carry 0

> Result: D

#### Column 2: 9 + 8 = 17
- 17 ≥ 16 → 17 - 16 = 1 → write 1, carry 1
→ So: 9 + 8 = 17 → 1 (write), carry 1

> Result: 1, carry 1

#### Column 3: 7 + F + carry(1) = 7 + 15 + 1 = 23
- 23 ≥ 16 → 23 - 16 = 7 → write 7, carry 1

> Result: 7, carry 1

#### Column 4: C + 6 + carry(1) = 12 + 6 + 1 = 19
- 19 ≥ 16 → 19 - 16 = 3 → write 3, carry 1

> Result: 3, carry 1

#### Column 5: 4 + 5 + carry(1) = 4 + 5 + 1 = 10
- 10 in hex = A → write A, no further carry

> Result: A

---

Now, putting all together from left to right:

A 3 7 1 D

So:
$$
4C799_{16} + 56F84_{16} = A371D_{16}
$$

---

✔ Fill in the blanks:

#### Values:
- C = 12
- F = 15

#### Column-wise breakdown:

| Column | Digits Added | Sum | Subtract 16? | Digit Written | Carry |
|--------|--------------|-----|---------------|----------------|-------|
| 1 | 9 + 4 | 13 | No | D | 0 |
| 2 | 9 + 8 | 17 | 17 - 16 = 1 | 1 | 1 |
| 3 | 7 + F + 1 | 23 | 23 - 16 = 7 | 7 | 1 |
| 4 | C + 6 + 1 | 19 | 19 - 16 = 3 | 3 | 1 |
| 5 | 4 + 5 + 1 | 10 | No | A | 0 |

So:

Result:
- Column 1: 9 + 4 = 13 → 13 - 0 = D → Add 0
- Column 2: 9 + 8 = 17 → 17 - 16 = 1 → Add 1
- Column 3: 7 + 15 + 1 = 23 → 23 - 16 = 7 → Add 1
- Column 4: 12 + 6 + 1 = 19 → 19 - 16 = 3 → Add 1
- Column 5: 4 + 5 + 1 = 10 → 10 - 0 = A → Add 0

> Therefore: $ 4C799_{16} + 56F84_{16} = \boxed{A371D_{16}} $

---

Problem 2: Add $ E729F_{16} + 8CB29_{16} $

First, convert letters:
- B = 11
- C = 12
- E = 14
- F = 15

So:

```
E 7 2 9 F
+ 8 C B 2 9
---------------------
```

Again, from right to left (Column 1 to 5)

---

#### Column 1: F + 9 = 15 + 9 = 24
- 24 ≥ 16 → 24 - 16 = 8 → write 8, carry 1

> Result: 8, carry 1

#### Column 2: 9 + 2 + carry(1) = 9 + 2 + 1 = 12 → write C, carry 0

> Result: C, carry 0

#### Column 3: 2 + B + carry(0) = 2 + 11 = 13 → write D, carry 0

> Result: D, carry 0

#### Column 4: 7 + C + carry(0) = 7 + 12 = 19 → 19 - 16 = 3 → write 3, carry 1

> Result: 3, carry 1

#### Column 5: E + 8 + carry(1) = 14 + 8 + 1 = 23 → 23 - 16 = 7 → write 7, carry 1

> Result: 7, carry 1

Now, since there’s a carry of 1 at the end, we need an extra digit (Column 6):
→ Add 1 → write 1

So final result: 1 7 3 D C 8

Wait — order: from left to right:

- Column 6: 1
- Column 5: 7
- Column 4: 3
- Column 3: D
- Column 2: C
- Column 1: 8

So: 173DC8₁₆

---

✔ Final Answer:

$$
E729F_{16} + 8CB29_{16} = \boxed{173DC8_{16}}
$$

---

✔ Fill in the blanks:

#### Values:
- B = 11
- C = 12
- E = 14
- F = 15

#### Column-wise breakdown:

| Column | Digits Added | Sum | Subtract 16? | Digit Written | Carry |
|--------|--------------|-----|---------------|----------------|-------|
| 1 | F + 9 | 24 | 24 - 16 = 8 | 8 | 1 |
| 2 | 9 + 2 + 1 | 12 | No | C | 0 |
| 3 | 2 + B + 0 | 13 | No | D | 0 |
| 4 | 7 + C + 0 | 19 | 19 - 16 = 3 | 3 | 1 |
| 5 | E + 8 + 1 | 23 | 23 - 16 = 7 | 7 | 1 |
| 6 | 1 (carry) | 1 | No | 1 | 0 |

So:

Result:
- Column 1: F + 9 = 24 → 24 - 16 = 8 → Add 1
- Column 2: 9 + 2 + 1 = 12 → 12 - 0 = C → Add 0
- Column 3: 2 + B + 0 = 13 → 13 - 0 = D → Add 0
- Column 4: 7 + C + 0 = 19 → 19 - 16 = 3 → Add 1
- Column 5: E + 8 + 1 = 23 → 23 - 16 = 7 → Add 1
- Column 6: 1 + 0 + 0 = 1 → 1 → Add 0

> Therefore: $ E729F_{16} + 8CB29_{16} = \boxed{173DC8_{16}} $

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✔ Final Answers:

1. $ 4C799_{16} + 56F84_{16} = \boxed{A371D_{16}} $
2. $ E729F_{16} + 8CB29_{16} = \boxed{173DC8_{16}} $

You can now fill these into the worksheet boxes accordingly.

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