16-Bit Calculator

Add and subtract two 16-bit numbers in CircuitVerse.

Try the calculator Set A, B and the mode M, then read the 16-bit result and Cout. Can you make 16 bits overflow? Try FFFF + 0001, or subtract a bigger number from a smaller one and spot the borrow.

Live Circuit & Input Checker See an example

Project overview

16bits in each input, A and B

16one-bit full adders in a chain

Mmode switch: 0 adds, 1 subtracts

Coutcarry or borrow flag

Our calculator adds and subtracts two 16-bit numbers, A and B. It is built in CircuitVerse from sixteen one-bit full adders. The carry-out of each adder goes into the carry-in of the next one, starting at bit 0 (the rightmost bit) and ending at bit 15.

A mode switch called M picks the operation. Set M = 0 to add. Set M = 1 to subtract. When M = 1, the circuit flips every bit of B and adds 1, which gives A - B.

The circuit shows a 16-bit result and a carry-out called Cout. In add mode, Cout = 1 means the sum is too big for 16 bits (a carry). In subtract mode, Cout = 1 means no borrow (A is greater than or equal to B), and Cout = 0 means there was a borrow (A is less than B).

Our team

Group: G

Member	Contribution
Balanlay, Adam Samuel	[What this member did]
Fortes, Axel Dirk	[What this member did]
Gingging, Ria Fatima	[What this member did]
Gokotano, Ray Nathaniel	[What this member did]
Murry, Ralph	[What this member did]
Royo, Paolo	[What this member did]

How to use the calculator

Steps

Click Open in CircuitVerse and select Launch Simulator if it appears.
Set the 16-bit input A.
Set the 16-bit input B.
Set the mode M: 0 for addition, 1 for subtraction.
Read the 16-bit result and Cout.

Reading carry and borrow

Mode	Cout = 1	Cout = 0
M = 0 (add)	Carry	No carry
M = 1 (subtract)	No borrow	Borrow

Remember: in subtract mode the meaning of Cout is reversed. Cout = 0 means A is less than B.

The circuit

CircuitVerse diagram of the 16-bit calculator showing 32 top input pins for A and B, the mode switch on the far right, sixteen XOR gates feeding sixteen full adders connected in a carry chain, sixteen sum output pins along the bottom, and the carry-out pin at the bottom left.

Click the diagram to inspect it at full resolution.

Circuit test record

All 12 test cases and the mode-switch check tested in CircuitVerse:

Case	Mode	A	B	Expected result	Observed result	Expected status	Observed status	Pass/Fail
1	0 (Add)	`0000 0000 0000 0000` (0000)	`0000 0000 0000 0000` (0000)	`0000 0000 0000 0000` (0000)	`0000 0000 0000 0000` (0000)	Cout = 0 (No carry)	Cout = 0 (No carry)	Pass
2	0 (Add)	`0000 0000 0000 0010` (0002)	`0000 0000 0000 0011` (0003)	`0000 0000 0000 0101` (0005)	`0000 0000 0000 0101` (0005)	Cout = 0 (No carry)	Cout = 0 (No carry)	Pass
3	0 (Add)	`0000 0000 1111 1111` (00FF)	`0000 0000 0000 0001` (0001)	`0000 0001 0000 0000` (0100)	`0000 0001 0000 0000` (0100)	Cout = 0 (No carry)	Cout = 0 (No carry)	Pass
4	0 (Add)	`0111 1111 1111 1111` (7FFF)	`0000 0000 0000 0001` (0001)	`1000 0000 0000 0000` (8000)	`1000 0000 0000 0000` (8000)	Cout = 0 (No carry)	Cout = 0 (No carry)	Pass
5	0 (Add)	`1000 0000 0000 0000` (8000)	`1000 0000 0000 0000` (8000)	`0000 0000 0000 0000` (0000)	`0000 0000 0000 0000` (0000)	Cout = 1 (Carry)	Cout = 1 (Carry)	Pass
6	0 (Add)	`1111 1111 1111 1111` (FFFF)	`0000 0000 0000 0001` (0001)	`0000 0000 0000 0000` (0000)	`0000 0000 0000 0000` (0000)	Cout = 1 (Carry)	Cout = 1 (Carry)	Pass
7	0 (Add)	`0000 0000 0000 0101` (0005)	`0000 0000 0000 0011` (0003)	`0000 0000 0000 1000` (0008)	`0000 0000 0000 1000` (0008)	Cout = 0 (No carry)	Cout = 0 (No carry)	Pass
8	1 (Sub)	`0000 0000 0000 0101` (0005)	`0000 0000 0000 0011` (0003)	`0000 0000 0000 0010` (0002)	`0000 0000 0000 0010` (0002)	Cout = 1 (No borrow)	Cout = 1 (No borrow)	Pass
9	1 (Sub)	`0000 0001 0000 0000` (0100)	`0000 0000 0000 0001` (0001)	`0000 0000 1111 1111` (00FF)	`0000 0000 1111 1111` (00FF)	Cout = 1 (No borrow)	Cout = 1 (No borrow)	Pass
10	1 (Sub)	`0001 0010 0011 0100` (1234)	`0001 0010 0011 0100` (1234)	`0000 0000 0000 0000` (0000)	`0000 0000 0000 0000` (0000)	Cout = 1 (No borrow)	Cout = 1 (No borrow)	Pass
11	1 (Sub)	`0000 0000 0000 0000` (0000)	`0000 0000 0000 0001` (0001)	`1111 1111 1111 1111` (FFFF)	`1111 1111 1111 1111` (FFFF)	Cout = 0 (Borrow)	Cout = 0 (Borrow)	Pass
12	1 (Sub)	`0000 0000 0000 0011` (0003)	`0000 0000 0000 0101` (0005)	`1111 1111 1111 1110` (FFFE)	`1111 1111 1111 1110` (FFFE)	Cout = 0 (Borrow)	Cout = 0 (Borrow)	Pass
Mode-Switch	0 → 1	`0000 0000 0000 0101` (0005)	`0000 0000 0000 0011` (0003)	`0008` → `0002`	`0008` → `0002`	Cout = 0 → Cout = 1	Cout = 0 → Cout = 1	Pass

Worked examples

Example 1: addition, 00FF + 0001 (Test Record Case 3)

Mode M = 0 (add)
A 0000 0000 1111 1111 (hex 00FF, decimal 255)
B 0000 0000 0000 0001 (hex 0001, decimal 1)
Expected 0100, carry 0
Observed 0100, Cout = 0
Meaning 255 + 1 = 256. It fits in 16 bits, so there is no carry.

Example 2: subtraction, 0003 - 0005 (Test Record Case 12)

Mode M = 1 (subtract)
A 0000 0000 0000 0011 (hex 0003, decimal 3)
B 0000 0000 0000 0101 (hex 0005, decimal 5)
Expected FFFE, borrow 1
Observed FFFE, Cout = 0, so there is a borrow
Meaning FFFE is 65,534. 65,534 - 65,536 = -2, which is 3 - 5. The borrow shows that A is less than B.

Open the live circuit

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Open in CircuitVerse

Calculator

Input checker

Enter exactly 16 binary digits (only 0 and 1) in each field. Keep the leading zeros. This page only checks your entries. CircuitVerse does the calculation.