Multiply the bases. Show work
Consider the product of 232 × 32 in base 4 system
In base 4 system there are only four digits, {0, 1, 2, 3}
Consider product of 232 × 2 first.
Explanation:
The product of 232 and 2
1) 2 × 2 = 410 is equivalent to 10 in base 4 system
So take 0 (zero) below and carry 1
2) Now 3 × 2 = 610 = 124
Adding previous carry to it, gives 124 + 14 = 134
So take 3 below and carry 1
3) Now 2 × 2 = 410 = 104
Adding previous carry to it, gives 104 + 14 = 114
So take 11 below as there is no number further to add carry.
Now the product of 232 and 3
Explanation:
4) 3 × 2 = 610 = 124
So carry = 1 , and take 2 below
5) 3 × 3 = 910 = 214
Adding previous carry 1, gives 214+ 14 = 224
So carry = 2, and take 2 below
6) 3× 2 = 610 = 124
Adding previous carry 2, gives 124+ 24 = 204
Write it down 20 below, as there is no further place to add carry
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