Answer:
1B2 = 1 × sixteen2 + B × sixteen1 + 2 × sixteen0 1B2 = 110 × 162 + 1110 × 161 + 210 × 160 1B2 = 110 × 25610 + 1110 × 1610 + 210 ×110 1B2 = 25610 + 17610 + 210 1B2 = 43410
1B2 = 1 × sixteen2 + B × sixteen1 + 2 × sixteen0 1B2 = 110 × 162 + 1110 × 161 + 210 × 160 1B2 = 110 × 25610 + 1110 × 1610 + 210 ×110 1B2 = 25610 + 17610 + 210 1B2 = 43410
You already know how in base ten to multiply a number by 10: add a zero to the end. So 83 × 10 = 830. This works because:
83 = 8 × 101 + 3 × 100
83 × 10 = ( 8 × 101 + 3 × 100 ) × 10
= 8 × 102 + 3 × 101
= 830
The same trick works in any base: if a number is represented by (say) XYZ in base B, then XYZ0 represents that number times B.
What is sixteen times 8B3 ?