Half subtractor, Full Subtractor, Binary Multiplier
- 2. 2 Contents/Key Points Half subtractor ‑ Half Subtractor Truth Table, Diagram & Applications Full subtractor ‑ Full Subtractor Truth Table, Diagram & Applications Binary Multiplier ‑ 2-bit Multiplier Circuit Diagram & Output ‑ 3-bit Multiplier Circuit Diagram & Output ‑ 4-bit Multiplier Circuit Diagram & Output ‑ Binary Multiplier Application
- 3. 3 Subtractor Circuit In digital electronics, a subtractor is a combinational circuit that performs subtraction of binary numbers. What does a Subtractor do? It takes two binary inputs and subtracts one from the other, producing: A difference (the result) A borrow (if needed, like a carry in addition) Types of Subtractors: 1. Half Subtractor & 2. Full Subtractor.
- 4. 4 Half Subtractor A half subtractor is a digital logic circuit that performs the binary subtraction of two single-bit binary numbers. It has two inputs, A and B, and two outputs, Difference and Borrow. The Difference output represents the result of subtracting B from A, while the Borrow output indicates whether a borrow is needed when A is smaller than B. The output equation: Difference = A'B+AB' Borrow = A'B
- 6. 6 Full Subtractor A Full Sub-tractor is a combinational circuit used to perform binary subtraction. It has three inputs: A (Minuend) B (Subtrahend) B-IN (Borrow-in from the previous stage) It produces two outputs Difference (D): The result of the subtraction. D = (A B) Bin ⊕ ⊕ Borrow-out (B-OUT): Indicates if a borrow is needed for the next stage. Bout = Bin (A ⊕ B)' + A'B
- 7. 7 Full Subtractor Circuit Diagram
- 8. 8 Binary Multiplier A binary multiplier is a combinational logic circuit that performs the multiplication of two binary numbers (0 and 1). The two binary numbers or the two binary inputs used in the binary multiplication are multiplicand and multiplier to get the binary product as a result.
- 9. 9 Key Components AND gates Used to generate the partial products by performing bitwise AND operations between the multiplicand and the multiplier bits. Binary adders (full and half adders) Used to sum up the partial products to obtain the final product. Registers Often used to store the input numbers and the intermediate results during the multiplication process.
- 10. 10 Binary Multiplier Types The following are the binary multiplier types: 1. 2-bit multiplier or 2×2 Binary multiplier – 2-bit multiplier using 2-bit full adder. – 2-bit multiplier using individual single-bit adders. 2. 3-bit multiplier or 3×3 binary multiplier – 3-bit multiplier using 3-bit full adders. – 3-bit multiplier using single-bit adders. 3. 4-bit multiplier or 4×4 binary multiplier – 4-bit multiplier using 4-bit full adders.
- 11. 11 2-bit multiplier (2×2 Binary multiplier) A 2-bit multiplier is a digital circuit that multiplies two 2-bit binary numbers and produces a binary product. It takes two inputs: A = A1 A0(2 bits) B = B1 B0 (2 bits) The product will be 4 bits long: P = P3 P2 P1 P0 (4 bits)
- 12. 12 3-bit Multiplier A 3-bit multiplier is a digital circuit that multiplies two 3-bit binary numbers and produces a 6-bit binary product. It takes two inputs: A = A2 A1 A0(3 bits) B = B2 B1 B0 (3 bits) The product will be 6 bits long: P = P5 P4 P3 P2 P1 P0 (6 bits)
- 13. 13 4-bit Multiplier A 4-bit multiplier is a digital circuit that multiplies two 4-bit binary numbers and produces a 8-bit binary product. It takes two inputs: A = A3 A2 A1 A0(4 bits) B = B3 B2 B1 B0 (4 bits) The product will be 8 bits long: P = P7 P6 P5 P4 P3 P2 P1 P0 (8 bits)
- 14. 14 Binary Multiplier Applications Digital Signal Processing: Used in audio and video processing, filtering, and modulation/demodulation. Computer Arithmetic: A fundamental component in CPUs and other processors for performing arithmetic operations. Communication Systems: Used in modulation, demodulation, mixing, and phase discrimination.
- 15. 15 Any Question?
- 16. 16 Thank You