Addition of two SD numbers

Question

t[i+1] = (ds>=D?1:(ds<=−D?−1:0));

we got this expression for calculating a transfer digit array.

but X = (4,-5,3,6) Y= (1,-2,3,6)

but on page 18 we got transfer digit as = [(0, −1, 1, 1, 0)] but when calculating by self I am getting [0,0,-1,1,1]

t[0] = 0;

t[1] = 4+1>=6 false ...> 5<= -6 false then 0

t[2] = -5-2 >= 6 false ...> -7<=-6 true then -1

t[3] = 3+3>=6 true then 1

t[4] = 6+6>=6 true then 1.

can you clarify this

Answer 1

The calculation on page 18 is correct and is done in detail as shown below. It seems to me that you were reading the digits in the wrong order, since (4,-5,3,6) has most significant digit 4 which you consider as least significant digit. 

The computation should be as follows for the signed digit numbers to base B=10 with digit set -6,...,+6:

    x[0] := 6
    x[1] := 3
    x[2] := -5
    x[3] := 4

    y[0] := 6
    y[1] := 3
    y[2] := -2
    y[3] := 1

For them, we compute the transfer digits in a first step:

    t[0] := 0
    t[1] := (x[0]+y[0]>=6?1:(x[0]+y[0]<=-6?-1:0)) = (12>=6?1:...) = 1
    t[2] := (x[1]+y[1]>=6?1:(x[1]+y[1]<=-6?-1:0)) = ( 6>=6?1:...) = 1
    t[3] := (x[2]+y[2]>=6?1:(x[2]+y[2]<=-6?-1:0)) = (-7>=6?1:(-7<=-6?-1:0)) = -1
    t[4] := (x[3]+y[3]>=6?1:(x[3]+y[3]<=-6?-1:0)) = (5>=6?1:(5<=-6?-1:0)) = 0

Hence, we compute the sum digits as

    s[0] := x[0]+y[0]+t[0]-t[1]*10 = 2
    s[1] := x[1]+y[1]+t[1]-t[2]*10 = -3
    s[2] := x[2]+y[2]+t[2]-t[3]*10 = 4
    s[3] := x[3]+y[3]+t[3]-t[4]*10 = 4
    s[4] := t[4] = 0