Show the step-by-step calculation for multiplying CDA₁₆ by AD₁₆.

Question

ScanSolve AI Tutor · Accepted Answer

Let's break down hexadecimal multiplication. It's similar to decimal multiplication, but instead of carrying over 10s, you carry over 16s.

Here are the decimal equivalents for hexadecimal digits:
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15

When you multiply two hexadecimal digits:

Convert them to decimal.
Multiply the decimal numbers.
Convert the product back to hexadecimal. If the product is $16_{10}$ or greater, you'll have a remainder (which is the digit to write down) and a quotient (which is the carry to the next column).

Problem (a):

CDA_{16} \times AD_{16}

Multiply $CDA_{16}$ by $D_{16}$ .
We'll multiply each digit of $CDA_{16}$ by $D_{16}$ ( $13_{10}$ ), starting from the right.
- $D \times A$ : $13_{10} \times 10_{10} = 130_{10}$ . To convert $130_{10}$ to hexadecimal: $130 \div 16 = 8$ with a remainder of 2. So, we write down 2 and carry 8.
- $D \times D + \text{carry } 8$ : $13_{10} \times 13_{10} + 8_{10} = 169_{10} + 8_{10} = 177_{10}$ . To convert $177_{10}$ to hexadecimal: $177 \div 16 = 11$ with a remainder of 1. $11_{10}$ is $B_{16}$ . So, we write down 1 and carry $B$ .
- $D \times C + \text{carry } B$ : $13_{10} \times 12_{10} + 11_{10} = 156_{10} + 11_{10} = 167_{10}$ . To convert $167_{10}$ to hexadecimal: $167 \div 16 = 10$ with a remainder of 7. $10_{10}$ is $A_{16}$ . So, we write down $A7$ .
The first partial product is $A712_{16}$ .
Multiply $CDA_{16}$ by $A_{16}$ .
We'll multiply each digit of $CDA_{16}$ by $A_{16}$ ( $10_{10}$ ), starting from the right. Remember to shift one position to the left (add a 0 at the end).
- $A \times A$ : $10_{10} \times 10_{10} = 100_{10}$ . To convert $100_{10}$ to hexadecimal: $100 \div 16 = 6$ with a remainder of $4

Step-by-step solution