Ling adder

In electronics, a Ling adder is a particularly fast binary adder designed using H. Ling's equations and generally implemented in BiCMOS. Samuel Naffziger of Hewlett-Packard presented an innovative 64 bit adder in 0.5 μm CMOS based on Ling's equations at ISSCC 1996. The Naffziger adder's delay was less than 1 nanosecond, or 7 FO4.

Equations

Ling adder, architecture Skllansky, radix-2, 4-bit

In Borland Turbo Basic 1.1:
'--- Step 0 ------------ Warning ---------------------------------------
P00 = A0 OR B0 '1dt, Initial only CLA & Ling Propagate
G00 = A0 AND B0 '1dt, Initial CLA & Ling & PPA Generate
D00 = A0 XOR B0 '1dt, Only Ling Initial half bit generate
P10 = A1 OR B1 '1dt
G10 = A1 AND B1 '1dt
D10 = A1 XOR B1 '1dt
P20 = A2 OR B2 '1dt
G20 = A2 AND B2 '1dt
D20 = A2 XOR B2 '1dt
P30 = A3 OR B3 '1dt
G30 = A3 AND B3 '1dt
D30 = A3 XOR B3 '1dt
'--- Step 1, Ling Propagate and Generate ------
LG01 = G00 '1dt
LG11 = G10 OR G00 '2dt
LP11 = P10 '1dt, Sklansky architecture
LG21 = G20 '1dt, Sklansky architecture
LP21 = P20 AND P10 '2dt
LG31 = G30 OR G20 '2dt
'--- Step 2, Ling PseudoCarry ---------------------------
H0 = LG01 '1dt
H1 = LG11 '2dt
H2 = LG21 OR '4dt TTL, Sklansky architecture
' 1dt 1dt 2dt
H3 = LG31 OR '4dt TTL
' 2dt 2dt 2dt
'--- Sum -----------------------------------------
S0 = '1dt
S1 = OR '4dt TTL
S2 = OR '5dt TTL
S3 = OR '7dt TTL
S4 = '5dt TTL, S4=C4=Cout

Ling adder, architecture Kogge-Stone, radix-2, 4-bit

'--- Step 0 ------------ Warning ---------------------------------------
P00 = A0 OR B0 '1dt, Initial only CLA & Ling Propagate
G00 = A0 AND B0 '1dt, Initial CLA & Ling & PPA Generate
D00 = A0 XOR B0 '1dt, Only Ling Initial half bit generate
P10 = A1 OR B1 '1dt
G10 = A1 AND B1 '1dt
D10 = A1 XOR B1 '1dt
P20 = A2 OR B2 '1dt
G20 = A2 AND B2 '1dt
D20 = A2 XOR B2 '1dt
P30 = A3 OR B3 '1dt
G30 = A3 AND B3 '1dt
D30 = A3 XOR B3 '1dt
'--- Step 1 ----------------------------
LG01 = G00 '1dt, Ling Generate
LP11 = P10 AND P00 '2dt, Ling Propagate, Kogge-Stone architecture
LG11 = G10 OR G00 '2dt
LP21 = P20 AND P10 '2dt
LG21 = G20 OR G10 '2dt, Kogge-Stone architecture
LG31 = G30 OR G20 '2dt
'--- Step 2, Ling PsevdoCarry ----
H0 = LG01 '1dt
H1 = LG11 '2dt
H2 = LG21 OR '4dt TTL, Kogge-Stone architecture
' 2dt 2dt 1dt
H3 = LG31 OR '4dt TTL
' 2dt 2dt 2dt
'--- Sum -----------------------------------------
S0 = '1dt
S1 = OR '4dt TTL
S2 = OR '5dt TTL
S3 = OR '7dt TTL
S4 = '5dt TTL, S4=C4=Cout