Question

Derive the logic gates for a 2-bit Arithmetic Logic Unit (ALU) with four micro-operations:

1) Complete the table below by showing the select input bits and the necessary groupings. (5 points) Select Inputs Micro-Operation Description F = A-B-1 F = A + B +1 F = AVB F = ashl A Subtraction with borrow Addition with carry Logic OR Arithmetic shift left 2) Draw a detailed logic circuit of the ALU's arithmetic unit. (10 points)

Answer 1

S0 S1 are select lines used to select the operation

Select input Microoperation / Drescription -A-B-1 subtraction with 1 F = ATB+1 Carry Addition with Carry 1 F 2 AUB - - Logic OR F-ashla An' thmati Shift lebty

2)

ALU'S Arithmatic Unit Consists of ① Subtraction with Borrow unit Addition with carry. onit

for adder unit full adder is used to implement two bit adder

for full Adder Troth Table Carry A BC sum o som o 0 0 DO BL cool 111 A 1 1 o 0 6 1 0 100 101 Sum = A BOC BC ero of 11.12 . Carry A O A B+B C+CA 2 Carry Simplifizing ( AB)-C TAB

two full adder used to form a two bit adder as follows

Using Full adder, Implementation of 2-bit Adder given in fig. below Cin (Cin=1) A. Sumo Full Add u Bo Carry. full A1 Sump Carry Adder Bi Logic Expression of Full Addas es give bele Som. = A. B. Co Co= Carry Input Here in this case Everythilfe Carey input, cinal Carry AB + (AB) C logic diagram of 2-Bit Adder. •Sumo Ao Bo (in Carry. Sumi Carry, 'T Corry. BI

Full subtractor used to form a 2 bit subtractor

Too full subtractor Truth table Bornw out 1 Diff ABC oo1 o Diff 011 Bc 0 1: 0 1o1 o Diff - ABC Borrow "RC OLD lo A 1 1 . ĀB + ÃC + BC Borrow - Simplifizing - ABB - C + Ã B

Implemetation of 2-bit all subtractor Subtractor. using Full • it uses 2- Full subtractor Unit. Logic Expression of subtractor is given below. Subo 40 BOC Co = Borrow input Borrow out I A B + (ABB). C Borrow out = AR +AB.C. Using two units of full subtal for 2-bit subtractor implemented follows A. Diff. fortv1. Borrow outo Difft Borrow out, AI Bi Banyow.au. 2-bit subtractor coith Logic diagram of Borrow input -Diffe Ao B. Borrow out o diffi AM B. Borrow out 1

3)

logic circuit consists of OR unit and shift unit

following logic circuit is used to obtain OR operation between two bit A and B

Logic lirait consists of A ORB Hv) Ao Bo A out) D B.

while arithmetic left shift

MSB is replaced with previous significant bit while lowest significant bit (LSB)is replaced with logic Value zero

for shift deft for Arithmetic shif left MSB USB I AIA O 0 After Shift I A. operation

4)

MUX is used to select operation to be performed

two 4X1 Mux is used

S1 is MSB

S1 is LSB

logic blocks derived in part 2 and 3 are connected to MUX as follows

outputs out 1 and out 0 are obtained when operations are performed

1. SO Add LSB A Auto out (0) 9 Bit 1 S1 Diff 4:1 (B,B) B & Adder liffo I mux C. 13 FOR Shift (A, A) A (BBMB 루 Bit Subtrated So С. 1 म 1 Add Diff 4:1 difft out (1) MSB 1, Ao OR mux Bo 0 Ai SS. BI A Ao