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Ten’s Complement Subtraction: Calculating (72530−13250)(72530 - 13250)

Ten’s Complement Subtraction: Calculating (72530−13250)(72530 - 13250)

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Nov 4, 2026

To subtract using ten's complement arithmetic (analogous to two's complement subtraction), we typically:

  1. represent the subtrahend (the number being subtracted) in the required “digit width,”
  2. take its ten's complement to form the negative value,
  3. add it to the minuend, and
  4. apply the same kind of rule as in two’s complement about whether to discard or include the final carry (or its equivalent in base 10).

Because your instruction says “assume rules similar to those for two’s complement arithmetic,” we will follow the standard two’s-complement-like procedure adapted to base 10: add the ten’s complement and, if a carry-out occurs, discard it (no end-around carry), yielding the correct positive result—which is the behavior consistent with two’s complement when there is no need to represent a negative result.

We compute: 72530−13250=59280.72530 - 13250 = 59280.

A compact visual of the computation flow is:

Two’s Complement Subtraction (background for the analogy)

Ten’s Complement Subtraction (Two’s-Complement-Like Rules)

  1. 1
    Step 1

    We have 5-digit numbers (72530 and 13250), so we use a 5-digit base-10 complement system.

  2. 2
    Step 2

    Subtrahend is 1325013250.

  3. 3
    Step 3

    Compute each digit’s complement to 9, then add 1 (10’s complement method):

    • First (9’s complement): 13250→8674913250 \rightarrow 86749 (digitwise 9−d9-d).
    • Then add 1: 86749+1=8675086749 + 1 = 86750.
  4. 4
    Step 4

    72530+86750=15928072530 + 86750 = 159280.

  5. 5
    Step 5

    Because the sum is 6 digits, there is a carry-out beyond the 5-digit width. Under two’s-complement-like rules for subtraction (positive result case), we discard the carry-out and keep the lower 5 digits: Lower 5 digits of 159280159280 are 5928059280.

  6. 6
    Step 6

    Therefore, 72530−13250=5928072530 - 13250 = 59280.

Verification (sanity check)

Even though the question asks specifically for ten’s complement arithmetic, it’s good practice to confirm: 72530−13250=59280.72530 - 13250 = 59280.

So the complement-based result matches standard subtraction.

Tip: Computing 10’s complement cleanly

For base 10 with nn digits: 9’s complement + 1 gives 10’s complement: replace each digit dd by (9−d)(9-d), then add 1.

Warning: Carry-handling depends on representation rules

Different textbooks sometimes describe “end-around carry” differently. Your prompt says “assume rules similar to two’s complement,” so we use the two’s-complement behavior: for a correct positive result, discard the carry-out beyond the fixed digit width.

Subtraction via Ten’s Complement (Lifecycle)

Choose number of digits

1. Fix width

Use enough digits to represent both numbers (here: 5 digits)."

Compute 10’s complement

2. Negate subtrahend

Find 9’s complement digitwise, then add 1."

Minuend + (10’s complement)

3. Add

Perform the addition in base 10."

Apply carry-discard logic

4. Final rule

Discard carry-out beyond the chosen width to get the final digit pattern."

Digitwise Complement Snapshot (Key Intermediate Values)

Shows the key numeric states used in the ten’s complement subtraction.

Common Edge Cases

Knowledge Check

Question 1 of 4
Q1Single choice

Using 5-digit ten’s complement arithmetic, what is the 10’s complement of 13250?

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