Represent the following decimal numbers in 1-Byte format. Also find its signed
representation form, 1’s complement representation form and 2’s complement
representation form.
(i) 10 and – 10 (ii) 44 and – 44 (iii) 75 and – 75 (iv) 125 and – 125

Let's solve the problem by representing the given decimal numbers in a 1-byte (8-bit) binary format, and then find their signed, 1's complement, and 2's complement forms.

### (i) 10 and -10
1. **Positive 10 (Unsigned):**
   - Decimal: \(10\)
   - Binary: \(0000\_1010\)

2. **Negative 10 (Signed, 1's complement, and 2's complement):**
   - Signed (most significant bit indicates sign): \(1000\_1010\)
   - 1's Complement: Invert the binary digits of \(0000\_1010\) → \(1111\_0101\)
   - 2's Complement: Add 1 to the 1's complement: \(1111\_0101 + 1 = 1111\_0110\)

### (ii) 44 and -44
1. **Positive 44 (Unsigned):**
   - Decimal: \(44\)
   - Binary: \(0010\_1100\)

2. **Negative 44 (Signed, 1's complement, and 2's complement):**
   - Signed: \(1010\_1100\)
   - 1's Complement: Invert the binary digits of \(0010\_1100\) → \(1101\_0011\)
   - 2's Complement: Add 1 to the 1's complement: \(1101\_0011 + 1 = 1101\_0100\)

### (iii) 75 and -75
1. **Positive 75 (Unsigned):**
   - Decimal: \(75\)
   - Binary: \(0100\_1011\)

2. **Negative 75 (Signed, 1's complement, and 2's complement):**
   - Signed: \(1100\_1011\)
   - 1's Complement: Invert the binary digits of \(0100\_1011\) → \(1011\_0100\)
   - 2's Complement: Add 1 to the 1's complement: \(1011\_0100 + 1 = 1011\_0101\)

### (iv) 125 and -125
1. **Positive 125 (Unsigned):**
   - Decimal: \(125\)
   - Binary: \(0111\_1101\)

2. **Negative 125 (Signed, 1's complement, and 2's complement):**
   - Signed: \(1111\_1101\)
   - 1's Complement: Invert the binary digits of \(0111\_1101\) → \(1000\_0010\)
   - 2's Complement: Add 1 to the 1's complement: \(1000\_0010 + 1 = 1000\_0011\)

### Summary

| Decimal | Unsigned (Binary) | Signed (Binary) | 1's Complement | 2's Complement |
|---------|-------------------|-----------------|----------------|----------------|
| 10      | 0000_1010         | 1000_1010       | 1111_0101      | 1111_0110      |
| -10     | N/A               | 1000_1010       | 1111_0101      | 1111_0110      |
| 44      | 0010_1100         | 1010_1100       | 1101_0011      | 1101_0100      |
| -44     | N/A               | 1010_1100       | 1101_0011      | 1101_0100      |
| 75      | 0100_1011         | 1100_1011       | 1011_0100      | 1011_0101      |
| -75     | N/A               | 1100_1011       | 1011_0100      | 1011_0105      |
| 125     | 0111_1101         | 1111_1101       | 1000_0010      | 1000_0013      |
| -125    | N/A               | 1111_1101       | 1000_0012      | 1000_0014      |

Would you like any further details or explanations?

### Follow-up Questions:
1. What is the general method to convert a positive binary number to its negative counterpart using 2's complement?
2. How does the most significant bit determine the sign of a binary number in 1-byte format?
3. What is the difference between 1's complement and 2's complement?
4. Can you explain how the binary addition in 2's complement works for negative numbers?
5. How are overflows detected in signed binary arithmetic?
6. Why is 2's complement more commonly used than 1's complement in computer systems?
7. How would you represent the number -128 in 1-byte format?
8. What is the maximum positive number that can be represented in 1-byte signed binary?

#### Tip: 
Always remember that in a signed binary system, the leftmost bit indicates the sign of the number, with 0 for positive and 1 for negative.

Learn how to represent decimal numbers like 10, -10, 44, -44, 75, -75, 125, and -125 in 1-byte format. Understand their signed, 1's complement, and 2's complement representations with detailed examples and explanations.

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