We are using a 8-bit full adder to compute D, the sum of A and B, with

A=  A7A6A5A4A3A2A₁A₀ = 00110100

B =  B7B6B5B4B3B2B₁B₀ = 00111111

where the decimal number in subscript indicates the position of s binary number within the 8-bit word, with zero (instead of one in human's arithmetic system) being the first position of the digit of a binary number in Computing

When adding the two binary digits of A and B at the same position within the Word,, there will be a Sum digit and a Carry digit resulted; for example A0+ B0 will result in S0 and C0 so on and so forth for the remaining 7 binary digits of A and B.

Drag and drop the "0" or "1" at the bottom of this page into the text box of the S's and C's.

S0 =          Blank 1 Question 1                                                C0 =        Blank 2 Question 1
S1 =           Blank 3 Question 1                                                C1 =         Blank 4 Question 1
S2 =          Blank 5 Question 1                                                C2 =        Blank 6 Question 1
S3 =          Blank 7 Question 1                                                C3 =        Blank 8 Question 1
S4 =          Blank 9 Question 1                                                C4 =        Blank 10 Question 1
S5 =          Blank 11 Question 1                                                C5 =        Blank 12 Question 1
S6 =          Blank 13 Question 1                                                C6 =        Blank 14 Question 1
S7 =          Blank 15 Question 1                                                 C7 =       Blank 16 Question 1

To solve this, we perform the bit-by-bit addition for each corresponding bit of **A** and **B**, keeping track of the carry bits. Here's how to go through each step of the binary addition:

We are adding:

A = 00110100  
B = 00111111

Let's perform the addition from the least significant bit (position 0) to the most significant bit (position 7), calculating both the **Sum** (S) and **Carry** (C) for each position.

1. **Position 0 (A₀ + B₀ + Carry₀):**
   - A₀ = 0, B₀ = 1, no carry from the previous operation (C₀ = 0)
   - Sum S₀ = (0 + 1) = 1
   - Carry C₀ = 0 (since there was no overflow)

2. **Position 1 (A₁ + B₁ + Carry₁):**
   - A₁ = 0, B₁ = 1, C₀ = 0
   - Sum S₁ = (0 + 1) = 1
   - Carry C₁ = 0

3. **Position 2 (A₂ + B₂ + Carry₂):**
   - A₂ = 1, B₂ = 1, C₁ = 0
   - Sum S₂ = (1 + 1) = 0 (carry over 1 to the next position)
   - Carry C₂ = 1

4. **Position 3 (A₃ + B₃ + Carry₃):**
   - A₃ = 0, B₃ = 1, C₂ = 1
   - Sum S₃ = (0 + 1 + 1) = 0 (carry over 1 to the next position)
   - Carry C₃ = 1

5. **Position 4 (A₄ + B₄ + Carry₄):**
   - A₄ = 1, B₄ = 1, C₃ = 1
   - Sum S₄ = (1 + 1 + 1) = 1 (carry over 1 to the next position)
   - Carry C₄ = 1

6. **Position 5 (A₅ + B₅ + Carry₅):**
   - A₅ = 0, B₅ = 1, C₄ = 1
   - Sum S₅ = (0 + 1 + 1) = 0 (carry over 1 to the next position)
   - Carry C₅ = 1

7. **Position 6 (A₆ + B₆ + Carry₆):**
   - A₆ = 0, B₆ = 0, C₅ = 1
   - Sum S₆ = (0 + 0 + 1) = 1
   - Carry C₆ = 0

8. **Position 7 (A₇ + B₇ + Carry₇):**
   - A₇ = 0, B₇ = 0, C₆ = 0
   - Sum S₇ = (0 + 0 + 0) = 0
   - Carry C₇ = 0

---

### The results for the sum and carry bits are:

- **S₀ = 1**, **C₀ = 0**
- **S₁ = 1**, **C₁ = 0**
- **S₂ = 0**, **C₂ = 1**
- **S₃ = 0**, **C₃ = 1**
- **S₄ = 1**, **C₄ = 1**
- **S₅ = 0**, **C₅ = 1**
- **S₆ = 1**, **C₆ = 0**
- **S₇ = 0**, **C₇ = 0**

---

Would you like to go over any specific step in more detail or have any questions?

Here are 5 related questions to deepen your understanding:
1. How does carry propagation work in an 8-bit adder circuit?
2. What is the significance of carry look-ahead in binary addition?
3. How does a full adder differ from a half adder?
4. How would you modify the adder to work with signed numbers?
5. What happens in binary addition if both numbers exceed the 8-bit range?

**Tip:** Understanding binary addition is fundamental to digital circuits, where adders form the basis for arithmetic logic units in processors.

We are using an 8-bit full adder to compute D, the sum of A and B, with A= 00110100 and B = 00111111, where each digit of A and B at the same position results in a Sum digit and a Carry digit.

Explore binary addition using an 8-bit full adder circuit for the binary numbers A = 00110100 and B = 00111111. This detailed solution walks through each step of the addition process, including sum and carry calculations for each bit. Suitable for students in Grades 9-12 interested in digital logic and computer architecture.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation