Combinational Circuits: Adders, Subtractors, and Multipliers Quiz Quiz

Explore the fundamental principles of combinational circuits with a focus on adders, subtractors, and multipliers. This quiz assesses your understanding of key digital logic concepts, circuit functions, and practical design considerations within arithmetic circuits.

1. Half Adder Output Characteristics

   Which of the following correctly describes the outputs of a half adder for binary inputs A = 1 and B = 1?

   1. Sum = 1, Carry = 0
   2. Sum = 0, Carry = 0
   3. Sum = 0, Carry = 1
   4. Sum = 1, Carry = 1

   Explanation: For a half adder, when both inputs A and B are 1, the sum is 0 (since 1 + 1 in binary results in 0 with a carry) and the carry output is 1. The other options are incorrect: 'Sum = 1, Carry = 0' happens if only one input is 1, not both. 'Sum = 1, Carry = 1' is not possible for a half adder, as the sum and carry cannot both be 1 for the same input pair. 'Sum = 0, Carry = 0' occurs when both inputs are 0.

2. Full Subtractor Borrow Behavior

   In a full subtractor, what is the value of the borrow output when the inputs are Minuend = 0, Subtrahend = 1, and Borrow-In = 0?

   1. Borrow undefined
   2. 2
   3. 0
   4. 1

   Explanation: A full subtractor gives a borrow output of 1 in this case because subtracting 1 from 0 requires borrowing. '0' would be true only if the minuend is equal to or greater than the sum of subtrahend and borrow-in. '2' is not a valid binary borrow output. 'Borrow undefined' is incorrect as the borrow is well-defined for this input combination.

3. Parallel Binary Adder Speed Advantage

   Why does a parallel binary adder (such as a carry-lookahead adder) perform faster than a ripple carry adder for large bit-widths?

   1. It uses fewer logic gates
   2. It requires more adders in parallel
   3. It skips sum calculation
   4. It reduces carry propagation delay

   Explanation: A parallel binary adder is faster because it minimizes the time it takes for carries to propagate from one bit to the next, which is the main bottleneck in ripple carry adders. The option 'It uses fewer logic gates' is incorrect; parallel adders generally use more gates for higher speed. 'It requires more adders in parallel' does not directly address the reason for increased speed. 'It skips sum calculation' is incorrect as both adders must compute the sum.

4. 4x2 Binary Multiplier Output Analysis

   What is the maximum number of output bits produced by a 4-bit by 2-bit combinational binary multiplier?

   1. 8
   2. 7
   3. 4
   4. 6

   Explanation: Multiplying a 4-bit number by a 2-bit number can produce a result that is up to 6 bits long (since the maximum product is 1111 x 11 = 106 with a binary representation of 1101010, but only the lower 6 bits are necessary). '8' is more than required as 4+2=6 bits suffice. '7' is too high for these operand sizes, and '4' is insufficient for the largest possible product.

5. Carry Propagation in Adders

   In a 4-bit ripple carry adder, how does the carry generated by the least significant bit affect the calculation of the most significant bit’s sum?

   1. The sum is computed before the carry propagates
   2. The least significant bit's carry is ignored in MSB calculation
   3. The carry must propagate through each intermediate adder stage
   4. The carry directly sets the most significant bit to zero

   Explanation: The ripple carry adder gets its name because the carry output from each bit must pass through each stage sequentially—from the least significant to the most significant bit—which can slow calculations. The other options are inaccurate: the carry does not directly set the most significant bit to zero, nor is it ignored, and the sum cannot be completed before the carry reaches the final stage.