Test: Subtractors - Electronics and Communication Engineering (ECE) MCQ

A full subtractor is a combinational circuit that performs subtraction of two bits, one is minuend and other is subtrahend, taking into account borrow of the previous adjacent lower minuend bit. This circuit has three inputs and two outputs. The three inputs are minuend, subtrahend, and previous borrow. The two outputs represent the difference and output borrow.

A binary full-subtractor contains two half-subtractors and one OR gate.

Truth table for the full- subtractor is

Difference(D) = A̅ B̅ Bin + A̅ B B̅in + AB̅ B̅in + ABBin

D = Bin ⊕ (A ⊕ B)

Borrow(B) = A̅ B̅ Bin + A̅ B B̅in + A̅ B Bin + ABBin

B = (A̅ B̅ + AB)Bin + A̅ B

B = (A̅ ⊕ B)Bin + A̅ B

The Truth Table for a half subtractor is drawn as:

The Boolean expression for difference can be written as:

N = X̅ Y + XY̅

N = X ⊕ Y

And the Boolean expression for the borrow can be written as:

M = X̅ Y

Concept:

The truth table for a tristate buffer is as shown:

Observation:

If the “Enable” input signal is 1, the input is simply passed to the output.

If the “Enable” input signal is 0, the tristate buffer passes a high impedance signal that disconnects its output from the circuit.

Application:

When A = 0, Buffer 1 and Buffer 3 are enabled, and buffer 2 and 4 are disabled.

The input to the 4-bit subtractor will be Y and X respectively, such that the output is:

D = Y – X = 0010 – 0101

= 1101 with a borrow of 1, i.e. B_out = 1

In given question

Y₀ to y₇ are minterms

Concept:

A half subtractor is a combinational circuit that is used to perform the subtraction of two single-bit words.

It subtracts two single-bits A & B and produces difference d & borrow b. 

The equation for half subtractor is :

d = A'B+AB' or A ⊕ B

b = A'B

Truth Table for half subtractor:

From the above circuit we get,

F = A⊕ B and G = A¯B

F implements the Difference and G implements the barrow. So the given circuit acts like a Half Subtractor 

For subtracting 1 from 0, we use to take a borrow from neighbouring bits because carry is taken into consideration during addition process.

Minuend and subtrahend are the two bits of input of a subtractor. If A and B are the two inputs of a subtractor then A is called minuend and B as subtrahend.

The sum and difference output of a full adder and a full subtractor are same. If A, B and C are the input of a full adder and a full subtractor then the output will be given by (A XOR B XOR C), respectively.

A full subtractor has 3 input bits and two outputs bits BORROW and DIFFERENCE. The full subtractor can be implemented using two half subtractors and an OR gate.