14.3.1 Hybrid Radix-2 Addition /96 Radix-2 signed-digit number unsigned conventional umber S<2.1>=X2.1>+Y where,X<r.a>=Xw-1.Xw-2Xw-3...Xo,Y=yw-1.yw-2Yw-3..Yo. X∈{1,0,1}， y∈{0,1} 11
11 14.3.1 Hybrid Radix-2 Addition S<2.1> = X<2.1> + Y where, X<r.a> = xW-1 .xW-2xW-3…x0 , Y = yW-1 .yW-2yW-3…y0 . xi {1,0,1} , yi {0,1} Radix-2 signed-digit number unsigned conventional umber
14.3.1 Hybrid Radix-2 Addition /96 The addition is carried out in two steps (1)The 1st step is carried out in parallel for all the bit positions i.An intermediate sum p;=xi+yi is computed, which lies in the range {1,0,1,2).The addition is expressed as: Xi yi=2t uir where t0,1}is the transfer digit,and is denoted as t+; uE{1,0}is the interim sum,and is denoted as-u. Let t.1=0,uw=0. (2)The sum digits s;are formed as follows: si t-1+-ui 12
12 14.3.1 Hybrid Radix-2 Addition The addition is carried out in two steps : (1) The 1st step is carried out in parallel for all the bit positions i. An intermediate sum pi = xi + yi is computed, which lies in the range {1, 0, 1, 2}. The addition is expressed as: xi + yi = 2ti + ui , where ti {0,1} is the transfer digit, and is denoted as ti +; ui {1,0} is the interim sum, and is denoted as -ui - . Let t-1=0, uW=0. (2) The sum digits si are formed as follows: si = ti-1 + - ui -
14.3.1 Hybrid Radix-2 Addition /966 Digit sets involved in hybrid radix-2 addition Digit Radix 2 Digit Set Binary Code 1,0,1 Xi-Xi Y {0,1} Y Pi=Xi+yi 1,0,1,2} 2t:+u u 1,0} -U; t {0,1} t 5;=u+t-1 1,0,1 5,*-5 13
13 14.3.1 Hybrid Radix-2 Addition Digit sets involved in hybrid radix-2 addition
4 14.3.1 Hybrid Radix-2 Addition 96 Eight-digit hybrid radix-2 adder ya 96 ys ya y yo + + X6X6 X5 X5 X I X 4 PPM PPM PPM PPM PPM PPM PPM PPM 8?87 8686 85858484 8383 8182 8131 8080 14
14 14.3.1 Hybrid Radix-2 Addition Eight-digit hybrid radix-2 adder
96 Mybrid Radix-2 Addition Examples 4 bit hybrid radix-2 addition ▣1 7+7 ■2 7+1 ▣3 15+3 15
15 Hybrid Radix-2 Addition Examples 4 bit hybrid radix-2 addition 1 7+7 2 7+1 3 15+3