Subtractor design in Verilog - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a subtractor in digital logic?

A subtractor is a digital circuit that performs subtraction of two binary numbers. It outputs the difference and borrow bits.

beginner

What is the difference between a half subtractor and a full subtractor?

A half subtractor subtracts two bits and produces a difference and borrow. A full subtractor subtracts three bits (including borrow-in) and produces difference and borrow-out.

intermediate

Write the Verilog module header for a 1-bit full subtractor.

module full_subtractor(input a, input b, input bin, output diff, output bout);

intermediate

What is the Boolean expression for the difference output in a full subtractor?

Difference (diff) = a ^ b ^ bin

intermediate

How is the borrow output (bout) calculated in a full subtractor?

Borrow out (bout) = (~a & b) | (b & bin) | (~a & bin)

Which of the following is true about a half subtractor?

A It subtracts three bits including borrow-in.

B It multiplies two bits.

C It adds two bits and produces sum and carry.

D It subtracts two bits and produces difference and borrow.

A half subtractor subtracts two bits and outputs difference and borrow.

In Verilog, which keyword is used to define a module?

A module

B function

C class

D package

The keyword 'module' is used to define a module in Verilog.

What is the difference output of a full subtractor when inputs a=1, b=0, bin=1?

A 1

B 0

C Undefined

D 2

Difference = a XOR b XOR bin = 1 XOR 0 XOR 1 = 0.

Which expression correctly represents borrow out in a full subtractor?

A (~a & b) | (b & bin) | (~a & bin)

B a & b & bin

C a | b | bin

D a XOR b XOR bin

Borrow out is calculated as (~a & b) | (b & bin) | (~a & bin).

What does 'bin' stand for in a full subtractor?

A Boolean input

B Binary input

C Borrow input

D Bit input

'bin' stands for borrow input, the borrow from the previous subtraction.

Explain the difference between a half subtractor and a full subtractor and their typical uses.

Think about how many inputs each subtractor handles and why borrow input matters.

Describe how to implement a 1-bit full subtractor in Verilog including inputs, outputs, and logic expressions.

Recall the Boolean formulas for difference and borrow and how to write them in Verilog.

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