How is an n-bit binary parallel adder built?

From n full adders in cascade, each carry out feeding the next higher carry in

From one full adder used n times with a clock

From n half adders in parallel with no carry links

From n OR gates and one XOR gate

What is the main limitation of the binary parallel adder?

Ripple carry delay: worst case is n times one stage carry delay

It cannot add numbers larger than 4 bits

It gives wrong sums for odd inputs

How can a parallel adder be made to subtract using 2's complement?

Put XOR gates on the B inputs and set C0 = 1

Put AND gates on the A inputs and set C0 = 0

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Short note: binary parallel adder

Short answer

A binary parallel adder adds two n-bit numbers using n cascaded full adders with simultaneous inputs. Each stage: Si = Ai⊕Bi⊕Ci, Ci+1 = AiBi + Ci(Ai⊕Bi). ICs like 7483 (4-bit) are cascaded. Limitation is ripple-carry delay, which carry look-ahead overcomes.

Write a short note on binary parallel adder.

A binary parallel adder is a combinational circuit that adds two n-bit binary numbers with all bits applied at the same time. It is made of $n$ full adders in cascade; the carry output of each full adder goes to the carry input of the next higher stage.

  A3 B3      A2 B2      A1 B1      A0 B0
 +-----+    +-----+    +-----+    +-----+
 | FA3 |<C3-| FA2 |<C2-| FA1 |<C1-| FA0 |<- C0
 +-----+    +-----+    +-----+    +-----+
  |   |        |          |          |
 C4   S3       S2         S1         S0

Each stage: $S_i = A_i \oplus B_i \oplus C_i$ , $C_{i+1} = A_iB_i + C_i(A_i \oplus B_i)$ .

Operation: FA0 adds the LSBs with $C_0$ (0 for plain addition); its carry goes to FA1, and so on. The result is $C_4S_3S_2S_1S_0$ . Example: $0101 + 0011 = 01000$ (5 + 3 = 8).

Features and uses:

IC 7483/74283 is a 4-bit binary parallel adder; ICs are cascaded ( $C_4$ to next $C_0$ ) for 8, 12, 16 bits.
With XOR gates on B and $C_0 = 1$ it becomes an adder/subtractor (2's complement).
Used in multipliers, BCD adders and the ALU.

Limitation: carry propagation (ripple) delay; worst-case delay is $n \times$ one-stage carry delay. A carry look-ahead adder overcomes this.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Short note: binary parallel adder

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