Question

If we had 20,000(subscript 10) memory locations, what would be the least number of address lines needed to describe each location? (Hint: Change 20,000 to binary or hex and determine the number of bits needed.)

Answer 1

For 20000 to convert to binary, we need to divide 20000 continuously by 2. and set the value of quotient in place of 20000 and the value of reminder for our bit or we can say binary digit.

We need to keep doing the same till quotient gets 0 and the binary number would be al the bits from down to top.

The calculation would clear it easily.

Decimal to Binary conversion

Division by 2	Quotient	Reminder
20000 / 2	10000	0
10000 / 2	5000	0
5000 / 2	2500	0
2500 / 2	1250	0
1250 / 2	625	0
625 / 2	312	1
312 / 2	156	0
156 / 2	78	0
78 / 2	39	0
39 / 2	19	1
19 / 2	9	1
9 / 2	4	1
4 / 2	2	0
2 / 2	1	0
1 / 2	0	1

So 20000₁₀ = 100111000100000₂

Since there are 15 bits in our resulting binary number. So, the least number of address lines is 15.

Solution ends.

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