The document discusses different types of single-bit adders and multi-bit adders built from them. It describes half adders, full adders, ripple carry adders and their delay properties. It then discusses different advanced adder circuits like carry lookahead adders, carry skip adders, carry select adders and carry save adders to reduce the delay. Verilog code examples are provided for full adders, ripple carry adders, carry lookahead adders and carry skip adders.

1. Peeyush Pashine (2011H140033H)

2. Single bit adders
Half Adder Full Adder

3. Full Adder
 Computes one-bit sum, carry
si = ai XOR bi XOR ci
ci+1 = aibi + aici + bici
 Adder delay is dominated by carry chain
 Ripple-carry adder: n-bit adder built from full adders.
 Delay of ripple-carry adder goes through all carry bits

4. 4-bit Ripple carry adder
T adder=(N-1)*Tcarry+ Tsum

5.  module fulladd(a,b,carryin,sum,carryout);
 input a, b, carryin; /* add these bits*/
 output sum, carryout; /* results */
 assign {carryout, sum} = a + b + carryin;
 /* compute the sum and carry */
 endmodule
 module nbitfulladd(a,b,carryin,sum,carryout);
 input[7:0] a, b; /* add these bits */
 input carryin; /* carry in*/
 output [7:0] sum; /* result */
 output carryout;
 wire [7:1] carry; /* transfers the carry between bits */
 fulladd a0(a[0],b[0],carryin,sum[0],carry[1]);
 fulladd a1(a[1],b[1],carry[1],sum[1],carry[2]);
 fulladd a2(a[2],b[2],carry[2],sum[2],carry[3]);
 fulladd a3(a[3],b[3],carry[3],sum[3],carryout);
 endmodule

7. Substractor

8. Subs tractor-adder

9. Static adder Circuit
Co= AB+BCi+ACi
S= ABCi+Co’(A+B+Ci)

10. Manchester carry chain adder
(a)Without pass transistors, (b)with pass transistors

11. Carry Look Ahead Adder

12. Carry Look Ahead Adder

13.  module sum(a,b,carryin,result);
 input a, b, carryin; /* add these bits*/
 output result; /* sum */
 assign result = a ^ b ^ carryin;
 /* compute the sum */
 endmodule
 module carry_block(a,b,carryin,carry);
 input [3:0] a, b; /* add these bits*/
 input carryin; /* carry into the block */
 output [3:0] carry; /* carries for each bit in the block */
 wire [3:0] g, p; /* generate and propagate */
 assign g[0] = a[0] & b[0]; /* generate 0 */
 assign p[0] = a[0] ^ b[0]; /* propagate 0 */
 assign g[1] = a[1] & b[1]; /* generate 1 */
 assign p[1] = a[1] ^ b[1]; /* propagate 1 */
 assign g[2] = a[2] & b[2]; /* generate 2 */
 assign p[2] = a[2] ^ b[2]; /* propagate 2 */
 assign g[3] = a[3] & b[3]; /* generate 3 */
 assign p[3] = a[3] ^ b[3]; /* propagate 3 */
 assign carry[0] = g[0] | (p[0] & carryin);
 assign carry[1] = g[1] | p[1] & (g[0] | (p[0] & carryin));
 assign carry[2] = g[2] | p[2] &
 (g[1] | p[1] & (g[0] | (p[0] & carryin)));
 assign carry[3] = g[3] | p[3] &
 (g[2] | p[2] & (g[1] | p[1] & (g[0] | (p[0] & carryin))));
 endmodule

14.  module carry_lookahead_adder(a,b,carryin,sum,carryout);
 input [3:0] a, b; /* add these together */
 input carryin;
 output [3:0] sum; /* result */
 output carryout;
 wire [4:1] carry; /* intermediate carries */
 /* build the carry-lookahead units */
 carry_block b0(a[3:0],b[3:0],carryin,carry[4:1]);
 /* build the sum */
 sum a0(a[0],b[0],carryin,sum[0]);
 sum a1(a[1],b[1],carry[1],sum[1]);
 sum a2(a[2],b[2],carry[2],sum[2]);
 sum a3(a[3],b[3],carry[3],sum[3]);

 endmodule

16. Carry skip adder
Tp=Tsetup+(M-1)*tcarry+(N/M-1)*Tbypass+ (M-1)*tcarry+Tsum

17. Manchester carry chain
implementation of carry skip adder

18.  module fulladd_p(a,b,carryin,sum,carryout,p);
 input a, b, carryin; /* add these bits*/
 output sum, carryout, p; /* results including propagate */
 assign {carryout, sum} = a + b + carryin;
 /* compute the sum and carry */
 assign p = a | b;
 endmodule
 module carryskip(a,b,carryin,sum,carryout);
 input [7:0] a, b; /* add these bits */
 input carryin; /* carry in*/
 output [7:0] sum; /* result */
 output carryout;
 wire [8:1] carry; /* transfers the carry between bits */
 wire [7:0] p; /* propagate for each bit */
 wire cs4; /* final carry for first group */


19.  fulladd_p a0(a[0],b[0],carryin,sum[0],carry[1],p[0]);
 fulladd_p a1(a[1],b[1],carry[1],sum[1],carry[2],p[1]);
 fulladd_p a2(a[2],b[2],carry[2],sum[2],carry[3],p[2]);
 fulladd_p a3(a[3],b[3],carry[3],sum[3],carry[4],p[3]);
 assign cs4 = carry[4] | (p[0] & p[1] & p[2] & p[3] & carryin);
 fulladd_p a4(a[4],b[4],cs4, sum[4],carry[5],p[4]);
 fulladd_p a5(a[5],b[5],cs4, sum[5],carry[6],p[5]);
 fulladd_p a6(a[6],b[6],cs4, sum[6],carry[7],p[6]);
 fulladd_p a7(a[7],b[7],cs4, sum[7],carry[8],p[7]);
 assign carryout = carry[8] | (p[4] & p[5] & p[6] & p[7] &
cs4);
 endmodule

21. Carry select adder
Tadd=Tsetup+M*tcarry+(N/M)*Tmux+Tsum

22. Carry save adder

23. Thank You