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3 votes
D716 x 2816

I.
21998

II.
219816

III.
21816

IV.
101016

User Jorge Luis
by
7.2k points

1 Answer

3 votes

Answer:

II. 2198₁₆

Explanation:

You want the product of D7 and 28 in hexadecimal.

Long multiplication

D7₁₆ × 28₁₆ = D7₁₆ × 20₁₆ + D7₁₆ × 8

= 1AE0₁₆ +6B8₁₆ = 2198₁₆

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Additional comment

A suitable calculator can figure this for you.

Here the multiplication can take advantage of the limited number of '1' bits in the binary representation of 28₁₆. Effectively, we only need to double D70 and halve D70 and add those values together.

The relevant decimal equivalents are A=10, B=11, D=13, E=14.

As with any place-value number system, numbers 1 place to the left have 16 times their value before shifting, where the base of the number system is 16.

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User MindSpiker
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