In digital arithmetic, binary multiplication follows the same positional, shift-and-add idea used in decimal multiplication; however, the digits are limited to 1s and 0s and partial products are therefore either the multiplicand (for a 1) or 0 (for a 0). Evaluate this statement.

Introduction / Context:
Binary multiplication is the cornerstone of digital arithmetic units such as multipliers and ALUs. Understanding how it mirrors decimal long multiplication, but with base-2 digits, helps in designing efficient hardware (array, Wallace tree) and software routines (shift-and-add algorithms).

Given Data / Assumptions:

• Binary digits are limited to 0 and 1.
• Positional value in base 2 follows powers of 2 (… 2^3, 2^2, 2^1, 2^0).
• Partial products are formed by gating the multiplicand with each multiplier bit and shifting by the bit position.

Concept / Approach:
Decimal long multiplication forms partial products by multiplying by each digit and shifting according to place value, then summing. Binary uses the same idea: for multiplier bit bi, the partial product is (bi * multiplicand) shifted left i places. Since bi is either 0 or 1, each partial product is either all zeros or an exact shifted copy of the multiplicand, simplifying hardware.

Step-by-Step Solution:
1) Write multiplicand and multiplier in binary.2) For each multiplier bit bi, compute partial product = (bi AND multiplicand) << i.3) Sum all partial products using binary adders.4) The process is structurally identical to decimal long multiplication except the digit set is {0,1}.

Verification / Alternative check:
Try a small example, e.g., 1011 (11) * 0110 (6). Partial products are either 0 or 1011 shifted appropriately; their sum equals 1000010 (66), which matches 11*6.

Why Other Options Are Wrong:
“Incorrect” contradicts the structural similarity. “Only repeated addition without shifting” ignores the standard long-multiplication implementation. “Requires decimal carries and base-10 correction” is irrelevant to base-2 arithmetic.

Common Pitfalls:
Confusing binary adders with decimal carry-corrected adders; forgetting to align partial products by bit position; mismanaging sign handling for signed numbers (handled via two’s complement or Booth encoding).

Final Answer:
Correct