4-Bit Adder and Subtractor

 One Circuit, Two Jobs: The 4-bit Adder-Subtractor Unlocked

Modern digital systems don’t just calculate 1s and 0s — they crunch multiple bits at once at blazing speed. That’s where 4-bit parallel arithmetic circuits come into play. From microcontrollers to CPUs, these circuits handle binary operations efficiently and accurately.

In this blog, we’ll break down:

  • How a 4-bit Parallel Adder works (with & without carry-in)
  • How a 4-bit Subtractor performs bitwise subtraction using full subtractors
  • How a single circuit can switch between addition and subtraction based on a control signal

1. 4-bit Parallel Adder:

A 4-bit parallel adder is a combinational circuit that adds two 4-bit binary numbers. It uses four full adders, one per bit, connected in a ripple-carry configuration.

Inputs:

  • A – 4 bit binary number

  • B – 4 bit binary number

  • C_in – Optional carry-in input (usually 0)

Outputs:

  • S – 4 bit binary sum

  • C_out – Final carry-out

Ripple-Carry Logic – Step by Step:

Let’s say:

  • A = 1011

  • B = 0110

  • C_in = 0

Here’s how the addition works:

  1. First Full Adder (LSB): A₀ + B₀ + Cin → S₀ + Carry₁

  2. Second Full Adder: A₁ + B₁ + Carry₁ → S₁ + Carry₂

  3. Third Full Adder: A₂ + B₂ + Carry₂ → S₂ + Carry₃

  4. Fourth Full Adder (MSB): A₃ + B₃ + Carry₃ → S₃ + C_out

With vs Without Carry-In:

Case 1: No Carry-In (Cin = 0)

This is a basic 4-bit addition with no previous carry.

Structure:

  • First Stage (LSB):
    Uses a Half Adder (HA) — because there's no carry-in at the first stage.

  • Remaining Stages (Bits 1 to 3):
    Use Full Adders (FA) — since they need to account for both input bits and the carry from the previous bit.

Case 2: With Carry-In (Cin = 1)

When a carry-in is provided (e.g., for multi-byte addition or in an adder-subtractor combo), all stages must handle carry.

Structure:

  • All 4 Stages (Bits 0 to 3):
    Use Full Adders (FA) — including the LSB — because carry-in (C_in) is treated as the third input to the first adder.

Why This Design?

  • Half Adder = Simpler, used only when no carry-in is needed.

  • Full Adder = Handles 3 inputs (A, B, Cin), required when carry propagation is involved.

Real-World Use:

Used in arithmetic logic units (ALUs), calculators, embedded controllers — anywhere binary addition is needed.

2. 4-bit Parallel Subtractor:

This circuit subtracts B from A using full subtractors in a ripple-borrow chain.

Inputs:

  • A – Minuend

  • B – Subtrahend

  • Bin – Initial borrow input (usually 0)

Outputs:

  • D – Binary difference

  • Bout – Final borrow-out

Subtraction – Step by Step:

Assume A = 1100 and B = 0011:

  1. First Subtractor (LSB): A₀ − B₀ − Bin → D₀ + Borrow₁

  2. Second Subtractor: A₁ − B₁ − Borrow₁ → D₁ + Borrow₂

  3. Continue till MSB...

Borrow Propagation:

Each subtractor passes its borrow to the next stage, just like a carry in addition.

Real-World Use:

Used in down counters, digital comparators, memory address calculations, and ALUs.

3. 4-bit Adder/Subtractor Combo Circuit:

Why build two circuits when one can do both addition and subtraction?

This circuit uses XOR gates and full adders to perform either operation based on a control signal.

Circuit Behavior:

Inputs: A, B, Control

Modified_B = B ⊕ Control  

Cin = Control  

  • If Control = 0 → Performs A + B
  • If Control = 1 → Performs A − B using 2’s complement method

Internal Structure:

  • 4 XOR gates to conditionally invert B

  • 4 full adders for the actual addition

  • One control input to switch modes

Real-World Use:

Used in ALUs, embedded processors, and compact arithmetic logic blocks.

Why This Matters?

These circuits lay the groundwork for:

  • ALUs in processors

  • High-speed digital systems

  • FPGA/Verilog-based design

  • Efficient use of logic gates and space

Mastering these 4-bit circuits opens the door to advanced VLSI, computer architecture, and embedded development.

We’re not done yet! Next, we’ll explore:

  • Carry Look-Ahead Adders (CLA) — speed up your addition
  • Borrow Look-Ahead Subtractors — smarter subtraction

Whether you're a student, hobbyist, or aspiring VLSI designer, these topics will upgrade your digital logic skills!

Stay tuned to Hobitronics.blog — where circuits don’t just add up… they subtract too!

Missed our previous blog on Application of subtractors

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