Question

In a \(16\text{k} \times 8\) microprocessor, the number of address and data lines respectively are:

• A. \(14,\ 8\)
• B. \(16,\ 8\)
• C. \(8,\ 16\)
• D. \(8,\ 14\)

Hint:

For a memory layout specified as \(M \times N\):
- Data Lines = \(N\)
- Address Lines = Find the power of 2 that equals \(M\) (since \(16\text{k} = 2^4 \times 2^{10} = 2^{14}\), the answer is 14).

Answer 1

The Correct Option is A

Concept: Memory configuration parameters are standardly written in the layout format \(M \times N\). This structural product expression defines two essential hardware properties of the memory array interface:
• Data Lines Component (\(N\)): The second value in the product expression represents the word size, which is the number of data bits stored within each individual memory location. This maps directly to the number of physical data lines required on the data bus.
• Address Lines Component (\(M\)): The first value represents the memory depth, which is the total number of unique addressable storage slots available. The number of address lines (\(n\)) required to decode this many unique locations satisfies the exponential equation: \[ 2^n = M \]

Step 1: Identifying the data lines count directly.
We are given a memory array configuration of \(16\text{k} \times 8\). Looking at the second parameter value: \[ \text{Word Size} = 8 \text{ bits} \] This means each unique memory location holds an 8-bit byte, requiring exactly 8 data lines.

Step 2: Calculating the number of required address lines.
Looking at the first parameter value, the total number of memory locations is: \[ M = 16\text{k} \] In digital systems engineering, the multiplier symbol \(\text{k}\) represents Kilo, which equals \(2^{10} = 1024\). Let us expand the value of \(M\) using base-2 values: \[ 16 = 2^4 \] \[ \text{k} = 2^{10} \] Now, combine these parts using standard exponent multiplication rules (\(2^a \times 2^b = 2^{a+b}\)): \[ M = 16 \times \text{k} = 2^4 \times 2^{10} = 2^{4+10} = 2^{14} \] We substitute this back into our core address lines equation (\(2^n = M\)): \[ 2^n = 2^{14} \] Equating the exponents directly gives: \[ n = 14 \text{ address lines} \] Therefore, the chip requires exactly 14 address lines and 8 data lines, matching Option (A).