1 / 13

Division

Division. Division. 1001 Quotient Divisor 1000 1001010 Dividend –1000 10 101 1010 –1000 10 Remainder. Binary division. Dividend = Quotient x Divisor + Remainder See how big a number can be subtracted Binary division is simpler.

rudyard-tate
Download Presentation

Division

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Division

  2. Division 1001 Quotient Divisor 1000 1001010 Dividend–1000 10 101 1010–1000 10 Remainder

  3. Binary division • Dividend = Quotient x Divisor + Remainder • See how big a number can be subtracted • Binary division is simpler Create a quotient bit (0 or 1) in each step

  4. Division hardware (Version 1)

  5. rem = rem - div if rem < 0 then // divisor too big rem = rem + div quo <<= 1 LSB(quo) = 0 else // can divide quo <<= 1 LSB(quo) = 1 fi div >>= 1 repeat unless done

  6. Binary division

  7. Binary division

  8. Observations • Half of the bits in divisor always 0 • Half of divisor is wasted • Instead of shifting divisor to the right, shift remainder to the left • Shift left first to save one iteration

  9. Division hardware (Version 2) ALU and divisor registers are reduced, remainder shifted left

  10. Start: Place Dividend in Remainder 1. Shift the Remainder register left1 bit. 2.Subtract the Divisor register from the left half of the Remainder register, & place the result in the left half of theRemainder register. Remainder > 0 Test Remainder Remainder < 0 3b. Restore the original value by adding the Divisor register to the left half of the Remainder register, &place the sum in the left half of the Remainder register. Also shift the Quotient register to the left, setting the new least significant bit to 0. 3a. Shift the Quotient register to the left setting the new rightmost bit to 1. nth repetition? No: < n repetitions Yes: n repetitions (n = 4 here) Done

  11. Observations on Divide Version 2 • Eliminate Quotient register by combining with Remainder as shifted left • Start by shifting the Remainder left as before. • Thereafter loop contains only two steps because the shifting of the Remainder register shifts both the remainder in the left half and the quotient in the right half • The consequence of combining the two registers together and the new order of the operations in the loop is that the remainder will shifted left one time too many. • Thus the final correction step must shift back only the remainder in the left half of the register

  12. Version 3 rem <<= 1 rem -= (div >> 32) if rem < 0 then rem += (div >> 32) rem <<= 1 LSB(rem) = 0 else rem <<= 1 LSB(rem) = 1 fi repeat unless done

  13. Division hardware (Version 3)

More Related