Subtractor design in Verilog - Step-by-Step Execution

Concept Flow - Subtractor design

Input A, Input B

↓

Calculate Difference = A - B

↓

Calculate Borrow

↓

Output Difference, Borrow

The subtractor takes two inputs A and B, calculates the difference and borrow, then outputs them.

Execution Sample

Verilog

module subtractor(
  input wire A,
  input wire B,
  output wire Diff,
  output wire Borrow
);
  assign Diff = A ^ B;
  assign Borrow = (~A) & B;
endmodule

This code defines a 1-bit subtractor that outputs the difference and borrow for inputs A and B.

Execution Table

Step	Input A	Input B	Diff (A XOR B)	Borrow ((~A) & B)	Explanation
1	0	0	0	0	Both inputs zero, difference 0, no borrow
2	0	1	1	1	A is 0, B is 1, difference 1, borrow needed
3	1	0	1	0	A is 1, B is 0, difference 1, no borrow
4	1	1	0	0	Both inputs 1, difference 0, no borrow

💡 All input combinations tested, outputs calculated accordingly

Variable Tracker

Variable	Input 0,0	Input 0,1	Input 1,0	Input 1,1
A	0	0	1	1
B	0	1	0	1
Diff	0	1	1	0
Borrow	0	1	0	0

Key Moments - 2 Insights

Why is borrow 1 only when A=0 and B=1?

Borrow is 1 when A is less than B, which happens only when A=0 and B=1 as shown in execution_table row 2.

Why is difference calculated as A XOR B?

Difference is the bitwise subtraction without borrow, which matches XOR logic, confirmed in all rows of execution_table.

Visual Quiz - 3 Questions

Look at the execution table, what is the borrow output when A=1 and B=0?

A 1

B 0

C Undefined

D Same as difference

💡 Hint

Check execution_table row 3 under Borrow column

At which input combination does the difference output become 0?

A A=0, B=1

B A=1, B=0

C A=1, B=1

D A=0, B=0

💡 Hint

Look at Diff column in execution_table rows 1 and 4

If input A changes from 0 to 1 while B is 1, how does borrow change?

A Borrow stays 1

B Borrow changes from 0 to 1

C Borrow changes from 1 to 0

D Borrow stays 0

💡 Hint

Compare Borrow values in execution_table rows 2 and 4

Concept Snapshot

Subtractor design in Verilog:
- Inputs: A, B (1-bit)
- Outputs: Diff = A XOR B, Borrow = (~A) & B
- Borrow is 1 when A < B
- Difference is bitwise subtraction without borrow
- Simple combinational logic for 1-bit subtractor

Full Transcript

This visual execution traces a 1-bit subtractor in Verilog. The subtractor takes inputs A and B, calculates difference as A XOR B, and borrow as (~A) & B. The execution table shows all input combinations and their outputs. Borrow is 1 only when A=0 and B=1, meaning A is less than B. Difference is 0 when inputs are equal. The variable tracker shows how values change with inputs. Key moments clarify why borrow behaves as it does and why difference uses XOR. The quiz tests understanding of borrow and difference outputs for given inputs. This helps beginners see how subtractor logic works step-by-step.

Practice

1.

What is the main function of a subtractor in digital circuits?

easy

A. To multiply two binary numbers

B. To add two binary numbers

C. To find the difference between two binary numbers

D. To store binary data

Solution

1. Step 1: Understand the subtractor's purpose

   A subtractor is designed to calculate the difference between two binary inputs.

2. Step 2: Compare with other operations

   Adders add, multipliers multiply, and storage units store data, so these are not subtractors.

3. Final Answer:

   To find the difference between two binary numbers -> Option C

4. Quick Check:

   Subtractor = Difference finder [OK]

Hint: Subtractor always calculates difference, not sum or product [OK]

Common Mistakes:

• Confusing subtractor with adder
• Thinking subtractor stores data
• Mixing subtractor with multiplier

2.

Which of the following is the correct Verilog module header for a 1-bit subtractor?

module subtractor(

easy

A. module subtractor(input a, input b, output diff, output borrow);

B. module subtractor(input a, b, output diff, borrow);

C. module subtractor(a, b, diff, borrow);

D. module subtractor(input a, input b, input diff, output borrow);

Solution

1. Step 1: Check correct input/output declaration

   Inputs must be declared with 'input' keyword and outputs with 'output'.

2. Step 2: Verify syntax correctness

   module subtractor(input a, input b, output diff, output borrow); correctly declares inputs and outputs with proper keywords and commas.

3. Final Answer:

   module subtractor(input a, input b, output diff, output borrow); -> Option A

4. Quick Check:

   Correct input/output syntax = module subtractor(input a, input b, output diff, output borrow); [OK]

Hint: Always declare inputs and outputs explicitly with keywords [OK]

Common Mistakes:

• Omitting input/output keywords
• Listing inputs and outputs without keywords
• Declaring outputs as inputs

3.

What is the output difference and borrow when inputs a=1 and b=0 are applied to this 1-bit subtractor module?

assign diff = a ^ b ^ borrow_in;
assign borrow_out = (~a & b) | (borrow_in & (~a ^ b));

Assume borrow_in = 0.

medium

A. diff = 0, borrow_out = 0

B. diff = 0, borrow_out = 1

C. diff = 1, borrow_out = 1

D. diff = 1, borrow_out = 0

Solution

1. Step 1: Calculate diff with given inputs

   diff = a ^ b ^ borrow_in = 1 ^ 0 ^ 0 = 1

2. Step 2: Calculate borrow_out with given inputs

   borrow_out = (~a & b) | (borrow_in & (~a ^ b)) = (0 & 0) | (0 & (0 ^ 0)) = 0

3. Final Answer:

   diff = 1, borrow_out = 0 -> Option D

4. Quick Check:

   1 - 0 = 1, no borrow needed [OK]

Hint: XOR inputs and borrow_in for diff; borrow if a < b [OK]

Common Mistakes:

• Forgetting borrow_in in diff calculation
• Misapplying borrow logic
• Mixing up a and b in borrow expression

4.

Identify the error in this Verilog code for a 1-bit subtractor:

module subtractor(input a, input b, output diff, output borrow);
  assign diff = a - b;
  assign borrow = (b > a);
endmodule

medium

A. Using '-' operator for bitwise subtraction is incorrect in Verilog

B. 'borrow' should be declared as 'output reg' instead of 'output'

C. The module lacks a clock input for synchronous operation

D. The borrow calculation logic is incorrect

Solution

1. Step 1: Check arithmetic operator usage

   Verilog '-' operator performs arithmetic subtraction but does not produce borrow output directly.

2. Step 2: Understand borrow signal generation

   Borrow must be calculated using logic expressions, not by comparing b and a with '>' operator.

3. Final Answer:

   Using '-' operator for bitwise subtraction is incorrect in Verilog -> Option A

4. Quick Check:

   Subtractor needs logic for borrow, not '-' operator [OK]

Hint: Use logic expressions for borrow, not '-' operator [OK]

Common Mistakes:

• Using arithmetic '-' expecting borrow output
• Ignoring borrow logic
• Assuming '>' operator works for borrow

5.

Design a 2-bit subtractor using two 1-bit subtractor modules connected in series. Which of the following correctly describes the borrow connection?

hard

A. The borrow input of the least significant bit subtractor connects to the borrow output of the most significant bit subtractor

B. The borrow output of the least significant bit subtractor connects to the borrow input of the most significant bit subtractor

C. The borrow outputs of both subtractors are connected together to form a single borrow output

D. The borrow inputs of both subtractors are tied to 0

Solution

1. Step 1: Understand borrow chaining in multi-bit subtractors

   Borrow from the lower bit subtractor must feed into the higher bit subtractor's borrow input.

2. Step 2: Verify connection direction

   The least significant bit's borrow output connects to the most significant bit's borrow input to propagate borrow correctly.

3. Final Answer:

   The borrow output of the least significant bit subtractor connects to the borrow input of the most significant bit subtractor -> Option B

4. Quick Check:

   Borrow chains from LSB to MSB [OK]

Hint: Borrow flows from lower to higher bits in subtractors [OK]

Common Mistakes:

• Connecting borrow inputs to zero for all bits
• Connecting borrow outputs together incorrectly
• Reversing borrow input/output connections