8051 singed number concept [compatibility mode]
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This document discusses signed number representation in 8051 microcontrollers. It explains that the most significant bit is used as the sign bit, with 0 representing positive numbers and 1 representing negative. Negative numbers are represented using two's complement. It provides examples of how positive and negative numbers are represented in binary. It also discusses overflow issues that can occur with signed number addition and when the overflow flag would be set. Finally, it presents a problem involving adding 5 numbers in BCD format and provides a solution.
8051 singed number concept [compatibility mode]
- 1. Prof. Nitin Ahire 1 Singed number concept in 8051 Microcontroller Nitin Ahire XIE Mahim
- 2. Prof. Nitin Ahire 2 Singed number concept • In everyday life, numbers are used that could be +Ve or –Ve • In the 8051 the MSB bit is set aside for the sign • If MSB(D7) =1 represent negative number • If MSB(D7) =0 represent positive numbers • The remaining bit D0 to D6 used for magnitude.
- 3. Prof. Nitin Ahire 3 As 8051 is a 8 bit controller here we consider the 8 bit numbers D7 D6 D1D2D3D4D5 D0 SIGN MAGNITUDE
- 4. Prof. Nitin Ahire 4 POSITIVE NUMBERS • The range of positive numbers can be represent by the format as shown in figure • It range from 0 to +127 0 0000 0000 +1 0000 0001 +5 0000 0101 +127 0111 1111
- 5. Prof. Nitin Ahire 5 NEGATIVE NUMBERS • For negative number D7=1 however the magnitude is represented in it’s 2’s compliment form • Steps 1 write the magnitude of the number in 8 bit binary 2 invert each bit 3 add one to it
- 6. Prof. Nitin Ahire 6 • Show how the 8051 would represent – 5 • Sol: 0000 0101 5 in 8-bit binary 1111 1010 invert bit 1111 1011 add 1 ( which is FB h )
- 7. Prof. Nitin Ahire 7 • Show how the 8051 would represent -128 • Sol: 1000 0000 0111 1111 1000 0000 ( which become 80h)
- 8. Prof. Nitin Ahire 8 Range of singed numbers • Decimal binary Hex -128 1000 0000 80 -127 1000 0001 81 -126 1000 0010 82 … ….. …… …. -2 1111 1110 FE -1 1111 1111 FF 0 0000 0000 00 +1 0000 0001 01 +2 0000 0010 02 … …… ……. …. +127 0111 1111 7F
- 9. Prof. Nitin Ahire 9 Overflow problem in signed number • What is an overflow? • If the result of an operation on the signed numbers is too large for the register, an overflow has occurred CY AC -OVRS0RS1FO P
- 10. Prof. Nitin Ahire 10 Example • Examine the following code and analyze the result MOV A,# +96 MOV R1, # +70 ADD A,R1
- 11. Prof. Nitin Ahire 11 Solution + 96 0110 0000 60h + 70 0100 0110 46h -------- --------------- +166 1010 0110 A6 and OV =1 according to CPU the result -90h which is wrong. ( OV = 1) +166 is not the valid signed number. ( 0 to +127)
- 12. Prof. Nitin Ahire 12 When is the OV flag set? 1. There is carry from D6 to D7 but no carry out of D7 (CY=0). 2. There is a carry from D7 out (CY=1) but no carry from D6 to D7.
- 13. Prof. Nitin Ahire 13 Example 1 • MOV A, #-2 (FEh) ( 1111 1110) • MOV R1,#-5 (FBh) ( 1111 1011) • ADD A,R1 (F9h=-7, 1111 1001correct), • So CPU generate OV=0
- 14. Prof. Nitin Ahire 14 Example 2 MOV A, #-128 ; (80H) MOV R4,#-2 (FEH) ADD A,R4 ( A=7EH =+127 INVALID ) So CPU generate OV =1
- 15. Prof. Nitin Ahire 15 Example 3 • MOV A,#+7; A=0000 0111 (A=07H) • MOV R1,#+18; R1= 0001 0010 (R1=12H) • ADD A,R1; A=0001 1001 (A=19H=+25) According to CPU, this is +25, which is correct (OV=0)
- 16. Prof. Nitin Ahire 16 • In any signed number addition OV indicates whether the result is valid or not • If OV=1, the result is erroneous • If OV=0, the result is valid.
- 17. Prof. Nitin Ahire 17 BCD ADDITION • Assume that 5 BCD data items are stored in RAM location starting at 40H, write a program to find the sum of all numbers. The result must be in BCD.
- 18. Prof. Nitin Ahire 18 • Data 40=(71) • 41=(11) • 42=(65) • 43=(59) • 44=(37)
- 19. Prof. Nitin Ahire 19 Solution • MOV R0,#40H MOV R2,05H CLR A MOV R7,A AGAIN:ADD A,@R0 DA A JNC NEXT INC R7 NEXT: INC RO DJNZ R2,AGAIN END