Add Hexadecimal Numbers: 2ABC + 78F2 | AI Research

Add Hexadecimal Numbers: $2ABC + 78F2$

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Nov 3, 2026

To add hexadecimal numbers, you use base-16 digit rules (digits $0$ – $9$ and $A$ – $F$ ) and the same “carry” concept as in decimal arithmetic, except that the carry happens when a column sum reaches $16$ (i.e., exceeds $F$ ). This course section will compute $2ABC + 78F2$ carefully by column, then verify the result via conversion to decimal.

Key learning terms: Hexadecimal Digit Carry Place value.

Mermaid: addition column alignment

We will compute:

2ABC_{16} + 78F2_{16} = ?_{16}

Hexadecimal Addition (carry/column method)

Step-by-step addition of $2ABC_{16}$ and $78F2_{16}$

1
Step 1
Write the numbers with matching digit columns (units, 16’s, 16^2, 16^3). Here both are 4 hex digits, so align as: 2 A B C and 7 8 F 2.
2
Step 2
Units column: $C + 2$ . Since $C=12$ (decimal), $12+2=14$ , which is hex $E$ . Write $E$ in the units place; carry is $0$ .
3
Step 3
16’s column: $B + F$ . Convert mentally: $B=11$ , $F=15$ so $11+15=26$ . In base 16, $26 = 16\cdot 1 + 10$ , so carry $1$ and digit $10$ which is hex $A$ . Write $A$ and carry $1$ .
4
Step 4
16^2 column: $A + 8 + carry(1)$ . $A=10$ , so $10+8+1=19$ . In base 16, $19=16\cdot 1 + 3$ , so carry $1$ and digit $3$ .
5
Step 5
16^3 column: $2 + 7 + carry(1)$ . $2+7+1=10$ , which is hex $A$ . No further carry beyond this (we stay within 4-digit result).
6
Step 6
Reading digits from highest to lowest: $A$ (16^3), $3$ (16^2), $A$ (16^1), $E$ (16^0). Therefore: $2ABC_{16}+78F2_{16}=A3AE_{16}.$

Column-wise hexadecimal addition (with carries)

Each column is summed in base 16; when the sum is $\ge 16$ , subtract 16 and carry 1.

Fast way to handle carries in hex

If a column sum is $16$ or more, subtract $16$ to get the digit, and carry $1$ to the next column. Example: $B(11)+F(15)=26\Rightarrow 26-16=10=A$ , carry $1$ .

Common checks and verification methods

Final answer

Therefore, the sum is:

2ABC_{16}+78F2_{16}=A3AE_{16}.

And in digit-by-digit form:

$C + 2 = E$
$B + F = A$ with carry $1$
$A + 8 + 1 = 3$ with carry $1$
$2 + 7 + 1 = A$

Mermaid summary of carries

Knowledge Check

Question 1 of 4

Q1Single choice

What is the units-column result when adding $2ABC_{16}+78F2_{16}$ ?

$C+2=E_{16}$

$C+2=F_{16}$

$C+2=D_{16}$

$C+2=10_{16}$

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