Subtractor design in Verilog - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of 4-bit subtractor module

What is the output of the following 4-bit subtractor module when inputs A = 4'b1010 and B = 4'b0011?

Verilog

module subtractor_4bit(input [3:0] A, input [3:0] B, output [3:0] Diff, output Borrow);
  assign {Borrow, Diff} = A - B;
endmodule

A Diff = 4'b1011, Borrow = 0

B Diff = 4'b1011, Borrow = 1

C Diff = 4'b0111, Borrow = 1

D Diff = 4'b0111, Borrow = 0

💡 Hint

Remember that Borrow is the carry out bit from subtraction in Verilog when using the assign with concatenation.

The subtraction 1010 (decimal 10) minus 0011 (decimal 3) equals 0111 (decimal 7) with no borrow (Borrow=0).

🧠 Conceptual

intermediate

Understanding borrow in binary subtraction

In a 1-bit subtractor, what does the borrow output represent?

A It is the sum of the two input bits.

B It shows if the subtraction result is zero.

C It indicates if the minuend bit is smaller than the subtrahend bit, requiring borrowing from the next higher bit.

D It indicates overflow in subtraction.

💡 Hint

Think about what happens when you subtract a larger bit from a smaller bit in binary.

Borrow signals that the current bit of the minuend is less than the subtrahend bit, so borrowing from the next higher bit is needed.

🔧 Debug

advanced

Identify the error in this subtractor module

What error will occur when compiling this Verilog subtractor module?

Verilog

module subtractor(input a, input b, output diff, output borrow);
  assign diff = a ^ b;
  assign borrow = ~a & b;
endmodule

A No error, module compiles and works correctly

B SyntaxError due to missing semicolon after borrow assignment

C Runtime error due to wrong borrow logic

D SyntaxError due to missing module end keyword

💡 Hint

Check each line carefully for missing punctuation.

The line assigning borrow is missing a semicolon at the end, causing a syntax error.

📝 Syntax

advanced

Correct syntax for 1-bit full subtractor

Which option correctly implements a 1-bit full subtractor in Verilog?

A

module full_subtractor(input a, input b, input bin, output diff, output bout);
  assign diff = a ^ b ^ bin;
  assign bout = (~a & b) | ((~a | b) & bin);
endmodule

B

module full_subtractor(input a, input b, input bin, output diff, output bout);
  assign diff = a ^ b ^ bin;
  assign bout = (~a & b) | ((~a & b) & bin);
endmodule

C

module full_subtractor(input a, input b, input bin, output diff, output bout);
  assign diff = a ^ b ^ bin;
  assign bout = (~a & b) & ((~a | b) | bin);
endmodule

D

module full_subtractor(input a, input b, input bin, output diff, output bout);
  assign diff = a ^ b ^ bin;
  assign bout = (~a | b) & ((~a & b) | bin);
endmodule

💡 Hint

Recall the borrow output formula for a full subtractor: bout = (~a & b) | ((~a | b) & bin)

Option A correctly implements the borrow logic for a full subtractor. Other options have incorrect boolean expressions.

🚀 Application

expert

Number of bits in output of subtractor with borrow

If you design an 8-bit subtractor module in Verilog that outputs the difference and borrow, how many bits should the borrow output have and why?

A 1 bit, because borrow indicates if the entire subtraction required borrowing from a higher bit

B 8 bits, one borrow bit per input bit

C 9 bits, to hold borrow and difference bits combined

D 0 bits, borrow is not needed in multi-bit subtractors

💡 Hint

Think about how borrow is represented in multi-bit subtraction.

The borrow output is a single bit indicating if the overall subtraction resulted in a borrow from a higher bit beyond the most significant bit.

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