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123 x 400 = 49200
123 x 50 = 6150
123 x 6 = 738
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56088
or
4----, 1 x 4, shift 4 times left
-8---, 2 x 4, shift 3 times left
-12--, 3 x 4, shift 2 times left
-5---, 1 x 5, shift 3 times left
-10--, 2 x 5, shift 2 times left
--15-, 3 x 5, shift 1 times left
--6--, 1 x 6, shift 2 times left
--12-, 2 x 6, shift 1 times left
---18, 3 x 6, no shift
--------
56088
For 64-bit multiply with 32-bit inputs resulting in 128-bit result:
AHAL x BHBL
(AH x BH) << 64
(AH x BL) << 32
(AL x BH) << 32
(AL x BL) << 0
A simple testcase 8-bit by 8-bit multiplication for 4 bit values of AH=1001, AL=1100, BH=0010, and BL=0101.
(AH x BH) << 8 = 1001 x 0010 << 8 = 0001001000000000
(AH x BL) << 4 = 1001 x 0101 << 4 = 0000001011010000
(AL x BH) << 4 = 1100 x 0010 << 4 = 0000000110000000
(AL x BL) << 0 = 1100 x 0101 << 0 = 0000000000111100
----------------------------------------------------
0001011010001100