(First-version division: ) Using a table similar to that shown in the Slide 8.10, calculate the octal unsigned 6-bit integer 768 divided by 138 using the hardware described in a figure of Slide 8.10. You should show the contents of each register on each step. Note that you have to actually show the differences in the procedures, not just the signs.

Slide 8.10

This slide shows the first version of the division hardware and algorithm, and an execution example 1110200112 ? Q:01002 & R:00102.

The figure gives the first version of the division hardware. The Divisor register, ALU, and Remainder register are all 64 bits wide, with only the Quotient register being 32 bits. The 32-bit divisor starts in the left half of the Divisor register and is shifted right 1 bit each iteration. The remainder is initialized with the dividend and zero-extended.

Control decides when to shift the Divisor and Quotient registers and when to write the new value into the Remainder register. The figure shows a division algorithm. If the difference is positive, the divisor did go into the dividend, so Step 2 generates a 1 in the quotient. Actually, there is the Remainder register, but no Difference register. The Remainder is restored if the difference is less than zero. These steps are repeated 32 times.

Using the above algorithm to complete the following table, which shows a 4-bit division of

11102 00112 ? Q: 01002 & R: 00102

Iteration Remainder Divisor Difference Quotient

0 Initialize

1 Shift and subtract

Assign & set or do nothing

2 Shift and subtract

Assign & set or do nothing

3 Shift and subtract

Assign & set or do nothing

4 Shift and subtract

Assign & set or do nothing

5 Shift and subtract

Assign & set or do nothing

6 Shift and subtract

Assign & set or do nothing

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