Diagram for the computation by the Engine of the Numbers of Bernoulli

Note G, with n = 4 substituted throughout — computing her B7 (modern B8)

A numeric instantiation of Ada Lovelace's original symbolic table (see Note G, p. 722 et seq.), with n = 4 substituted into every formula, and the three given constants set to B1 = 1/6, B3 = −1/30, B5 = 1/42. A register could not simply be overwritten: its value first had to be given off, and the store returned to zero before it could hold anything new. A red 0 follows a given off value. V6 and V7 give theirs off after Operation 19′ — which, strictly, presumes the engine already knows no third pass is coming, a fact only Operation 23′ actually confirms. In every row, the cell being written is shown in pink, and the cell or cells being read to produce it — seeding it, so to speak — are shown in light blue, both together in the same row. Green marks a step up, orange a step down. Operations 1, 7, and 8 are all seeding values without being a ±1 change (±V1) step, and are left in the plain (pink) style.
Operation Data Working Variables Result Variables
No.NatureActed uponReceivingStatement of Results V1V2V3 V4V5V6V7V8V9V10V11V12V13 V21V22V23V24
Operation 1 × V2, V3 V4, V5, V6 = 8 124 8880000000 1/6-1/301/420
Operation 2 V4, V1 V4 = 7 124 7880000000 1/6-1/301/420
Operation 3 + V5, V1 V5 = 9 124 7980000000 1/6-1/301/420
Operation 4 ÷ V4, V5 V11 = 7/9 124 79800007/900 1/6-1/301/420
Operation 5 ÷ V11, V2 V11 = 7/18 124 00800007/1800 1/6-1/301/420
Operation 6 V13, V11 V13 = -7/18 124 00800007/180-7/18 1/6-1/301/420
Operation 7 V3, V1 V10 = 3 124 008000300-7/18 1/6-1/301/420
Operation 8 + V2, V7 V7 = 2 124 008200300-7/18 1/6-1/301/420
Operation 9 ÷ V6, V7 V11 = 4 124 00820038/20-7/18 1/6-1/301/420
Operation 10 × V21, V11 V12 = 2/3 124 00820038/22/3-7/18 1/6-1/301/420
Operation 11 + V12, V13 V13 = 5/18 124 00820038/22/35/18 1/6-1/301/420
Operation 12 V10, V1 V10 = 2 124 00820028/205/18 1/6-1/301/420
Operation 13 V6, V1 V6 = 7 124 00720028/205/18 1/6-1/301/420
Operation 14 + V1, V7 V7 = 3 124 00730028/205/18 1/6-1/301/420
Operation 15 ÷ V6, V7 V8 = 7/3 124 00737/3028/205/18 1/6-1/301/420
Operation 16 × V8, V11 V11 = 28/3 124 00737/3028/2×7/305/18 1/6-1/301/420
Operation 17 V6, V1 V6 = 6 124 00630028/2×7/305/18 1/6-1/301/420
Operation 18 + V1, V7 V7 = 4 124 00640028/2×7/305/18 1/6-1/301/420
Operation 19 ÷ V6, V7 V9 = 3/2 124 006406/428/2×7/305/18 1/6-1/301/420
Operation 20 × V9, V11 V11 = 14 124 006406/428/2×7/3×6/405/18 1/6-1/301/420
Operation 21 × V22, V11 V12 = -7/15 124 00640028/2×7/3×6/4-7/155/18 1/6-1/301/420
Operation 22 + V12, V13 V13 = -17/90 124 00640028/2×7/3×6/4-7/15-17/90 1/6-1/301/420
Operation 23 V10, V1 V10 = 1 124 00640018/2×7/3×6/40-17/90 1/6-1/301/420
Operation 13′ V6, V1 V6 = 5 124 00540018/2×7/3×6/40-17/90 1/6-1/301/420
Operation 14′ + V1, V7 V7 = 5 124 00550018/2×7/3×6/40-17/90 1/6-1/301/420
Operation 15′ ÷ V6, V7 V8 = 1 124 00555/5018/2×7/3×6/40-17/90 1/6-1/301/420
Operation 16′ × V8, V11 V11 = 14 124 00555/5018/2×7/3×6/4×5/50-17/90 1/6-1/301/420
Operation 17′ V6, V1 V6 = 4 124 00450018/2×7/3×6/4×5/50-17/90 1/6-1/301/420
Operation 18′ + V1, V7 V7 = 6 124 00460018/2×7/3×6/4×5/50-17/90 1/6-1/301/420
Operation 19′ ÷ V6, V7 V9 = 2/3 124 004604/618/2×7/3×6/4×5/50-17/90 1/6-1/301/420
Operation 20′ × V9, V11 V11 = 28/3 124 000004/618/2×7/3×6/4×5/5×4/60-17/90 1/6-1/301/420
Operation 21′ × V23, V11 V12 = 2/9 124 00000018/2×7/3×6/4×5/5×4/62/9-17/90 1/6-1/301/420
Operation 22′ + V12, V13 V13 = 1/30 124 000000102/91/30 1/6-1/301/420
Operation 23′ V10, V1 V10 = 0 124 0000000001/30 1/6-1/301/420
Operation 24 V24, V13 V24 = -1/30 124 0000000001/30 1/6-1/301/42-1/30
Operation 25 + V1, V3 V3 = 5 125 0000000000 1/6-1/301/42-1/30
V21–V24 — the Bernoulli Numbers V11 — the running coefficient chain read this operation (seeding) written this operation step up (+V1) step down (−V1) resting zero, the row after a cast-off