1. Dept. of Electrical and Computer Eng., NCTU
Lab 3. 2-bit Comparator
Presenter: Chun-Hsien Ko
Contributors: Chung-Ting Jiang and Lin-Kai Chiu
Dept. of Electrical and Computer Eng., NCTU

2. Dept. of Electrical and Computer Eng., NCTU
What is comparator?
Design a 2-bit comparator
Input: A (2-bit) and B (2-bit)
Output: A=B, A>B, A<B
LAB: 2-bit Comparator
Dept. of Electrical and Computer Eng., NCTU

3. Dept. of Electrical and Computer Eng., NCTU
What is comparator?
If we only have 1-bit input A and B…
A>B, iff A=1, B=0
A=B, iff A=1, B=1 OR A=0,B=0
A<B, iff A=0, B=1
Truth table A B
A>B
A=B
A<B 1
Dept. of Electrical and Computer Eng., NCTU

4. Dept. of Electrical and Computer Eng., NCTU
Design a 2-bit comparator
Input: A [A1 A0] and B [B1 B0]
Output: A=B, A>B, A<B
For A>B:
{A1>B1, A0, B0 don’t care}
{A1=B1, A0>B0}
For A<B:
{A1<B1, A0, B0 don’t care}
{A1=B1, A0<B0}
For A=B:
{A1=B1, A0=B0} A1 B1
A1=B1 1
XNOR
Dept. of Electrical and Computer Eng., NCTU

5. Dept. of Electrical and Computer Eng., NCTU
Design a 2-bit comparator
How to implement XNOR?
Sum of Product: 𝑋=𝐴𝐵+ 𝐴 𝐵
𝑋= (𝐴 𝐵 + 𝐴 𝐵) A B X 1
Dept. of Electrical and Computer Eng., NCTU

6. Dept. of Electrical and Computer Eng., NCTU
Design a 2-bit comparator
How to implement XNOR?
𝑋= (𝐴 𝑋𝑂𝑅 𝐵)
𝑋= (𝐴 𝐵 + 𝐴 𝐵) A1 B1
A1=B1 1
NOR
Dept. of Electrical and Computer Eng., NCTU

7. Dept. of Electrical and Computer Eng., NCTU
Design a 2-bit comparator
For A=B:
{A1=B1, A0=B0}
X1: A1=B1
For A>B:
{A1>B1}
{A1=B1, A0>B0}
For A<B:
{A1<B1}
{A1=B1, A0<B0} X1
Dept. of Electrical and Computer Eng., NCTU

8. Dept. of Electrical and Computer Eng., NCTU
Implement a 2-bit comparator
Show the relation between two two-bit inputs, A and B
Design the circuit of A>B and A<B
Reuse the circuit of {A=B}
Equipment：
Use LED x 3 for display A>B, A=B, A<B
Use the following IC to implement Lab 6
7402 (NOR) x 1, 7408 (AND) x 2, (Inverter) x 1, 7432 (OR) x 1
Dept. of Electrical and Computer Eng., NCTU