本節選錄一系列只用到加(減)法與基本邏輯運算的式子.
a.
(譯註: by definition of 2's complement) 
(譯註: -x = -(NOT(NOT(x-1))+1) = -(-NOT(x-1)) = NOT(x-1) )c.
(譯註: by a.)
d.
(譯註: by a.)
e.
(譯註: by c.)
f.
(譯註: x+y = x-(-y) = x-(NOT(y)+1) = x-NOT(y)-1)
g.
(譯註: (x XOR y) = x+y with carry bits ignored,
2(x AND y) = carry bits )
h.
(譯註: (x OR y) = x+y - (x AND y) )
i.
(譯註: by g. and h.)
j.
(譯註: by a.)
k.
(譯註: (x XOR y) = x-y with borrow bits ignored,
2(NOT(x) AND y) = borrow bits)
l.
(譯註: first calculate 1-0 parts, then minus the 0-1 parts)
m.
(譯註: by k. and l.)
n.
(譯註: by definition of XOR)
o.
(譯註: (x AND NOT(y)) = the mask where x(i)=1 AND y(i)=0)
p.
q.
(譯註: NOT(x-y) = -(x-y)-1 = y-x-1)r.
(譯註: by q. - NOT(x) = -x-1)
s.
(譯註: NOT(x XOR y)
= NOT((x OR y) - (x AND y))
= (x AND y) - (x OR y) -1)
t.
(譯註: by s.)
u.
(譯註: by o.)
v.
(譯註: by p. (x AND y)
= (x - (x AND NOT(y)))
= x + (NOT(x AND NOT(y)) + 1)
= x + (NOT(x) OR y) + 1
= (NOT(x) OR y) + NOT(NOT(x)) + 1
= (NOT(x) OR y) - NOT(x) )
(d) 式可以循換地套用, 例如 -NOT(-NOT(x)) = x + 2, 依此類推. 同樣地, (e) 式也一樣: -NOT(-NOT(-x)) = x - 2. 我們可以利用這兩招對 x 任意增減任意常數.
(f) 式是 (j) 式的共軛式, (j) 式是使用加法來計算減法的常見技巧.
(g) 式跟 (h) 式出自 HAKMEN. (g) 式首先忽略進位地計算 x+y, 再補上忽略掉的進位.
對於兩個各位元獨立, 且為0與為1機率同高的亂數, 計算其加法的時候, 已被證明任一位元上發生進位的機率為 0.5. 當使用 (g) 式來計算兩數和的話, 任一位元上發生進位的機率小於 0.5.
(譯註: 原文此處估計為機率大於 0.25 且小於 0.5, 但證明不嚴謹故此處僅保留部份結論)
(k), (l) 式與 (g), (h) 式是共軛式. (k) 式首先忽略借位地計算 x-y (該借位的位元憑空加1, 不實際借位), 再扣回忽略掉的借位.
(n) 式只使用三種運算(AND, OR 跟減) 來實作 XOR 運算, 花費三個指令. 若只用 AND, OR 跟 NOT 的話, 須花費四個指令: (x XOR y) = (x OR y) AND NOT(x AND y).
與此相似, (u), (v) 兩式分別使用三種運算來實作 OR 跟 AND 運算, 花費三個指令.
