ArticleslgStudy

engineering

Subtractor

Subtractor is a engineering topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Subtractor rather than just read about it. In short: In electronics, a subtractor is a digital circuit that performs subtraction of numbers, and it can be designed using the same approach as that of an adder. The binary subtraction process is summarized below.

Subtractor — main illustration
Subtractor — illustration

Key takeaways

  • Subtractor belongs to engineering; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Subtractor to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Subtractor from memory before moving on to harder problems.

Reference excerpt

In electronics, a subtractor is a digital circuit that performs subtraction of numbers, and it can be designed using the same approach as that of an adder. The binary subtraction process is summarized below. As with an adder, in the general case of calculations on multi-bit numbers, three bits are involved in performing the subtraction for each bit of the difference: the minuend ( X i {\displaystyle X_{i}} ), subtrahend ( Y i {\displaystyle Y_{i}} ), and a borrow in from the previous (less significant) bit order position ( B i {\displaystyle B_{i}} ). The outputs are the difference bit ( D i {\displaystyle D_{i}} ) and borrow bit B i + 1 {\displaystyle B_{i+1}} . The subtractor is best understood by considering that the subtrahend and both borrow bits have negative weights, whereas the X and D bits are positive. The operation performed by the subtractor is to rewrite X i − Y i − B i {\displaystyle X_{i}-Y_{i}-B_{i}} (which can take the values -2, -1, 0, or 1) as the sum − 2 B i + 1 + D i {\displaystyle -2B_{i+1}+D_{i}} .

D i = X

⊕ Y i ⊕ B i {\displaystyle D_{i}=X_{}\oplus Y_{i}\oplus B_{i}}

B i + 1 = X i < ( Y i + B i ) {\displaystyle B_{i+1}=X_{i}<(Y_{i}+B_{i})} , where ⊕ represents exclusive or. Subtractors are usually implemented within a binary adder for only a small cost when using the standard two's complement notation, by providing an addition/subtraction selector to the carry-in and to invert the second operand.

− B = B ¯ + 1 {\displaystyle -B={\bar {B}}+1} (definition of two's complement notation)

A − B = A + ( − B ) = A + B ¯ + 1 {\displaystyle {\begin{alignedat}{2}A-B&=A+(-B)\\&=A+{\bar {B}}+1\\\end{alignedat}}}

Half subtractor

The half subtractors can be designed through the combinational Boolean logic circuits [2] as shown in Figure 1 and 2. The half subtractor is a combinational circuit which is used to perform subtraction of two bits. It has two inputs, the minuend X {\displaystyle X} and subtrahend Y {\displaystyle Y} and two outputs the difference D {\displaystyle D} and borrow out B out {\displaystyle B_{\text{out}}} . The borrow out signal is set when the subtractor needs to borrow from the next digit in a multi-digit subtraction. That is, B out = 1 {\displaystyle B_{\text{out}}=1} when X < Y {\displaystyle X<Y} . Since X {\displaystyle X} and Y {\displaystyle Y} are bits, B out = 1 {\displaystyle B_{\text{out}}=1} if and only if X = 0 {\displaystyle X=0} and Y = 1 {\displaystyle Y=1} . An important point worth mentioning is that the half subtractor diagram aside implements X − Y {\displaystyle X-Y} and not Y − X {\displaystyle Y-X} since B out {\displaystyle B_{\text{out}}} on the diagram is given by

… excerpt ends here. Continue reading the full article.

Illustrations

Subtractor: Figure 2: Half-subtractor using NAND gate only.
Figure 2: Half-subtractor using NAND gate only.
Subtractor illustration

Worked examples

Example 1 — a first encounter with Subtractor

Start with the simplest possible case. Write down what Subtractor claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Subtractor before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Subtractor ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Subtractor

In research
Subtractor appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Subtractor in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Subtractor is common in secondary-school and first-year university syllabi. It links to neighbouring topics Adders (electronics), Arithmetic logic circuits, Binary arithmetic, so understanding it makes those chapters shorter.
In everyday life
Look for Subtractor outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Subtractor in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Subtractor means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Subtractor out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Subtractor in simple terms?

In electronics, a subtractor is a digital circuit that performs subtraction of numbers, and it can be designed using the same approach as that of an adder. The binary subtraction process is summarized below.

Why does Subtractor matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Subtractor?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Subtractor.

Tags

  • Adders (electronics)
  • Arithmetic logic circuits
  • Binary arithmetic
  • Digital circuits
  • Subtraction

Keep exploring