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Coded Hex Calculator With signed & Unsigned Caluclations. Project Done By: Apurva Patel Vrajesh Patel Swapna Kalakonda. Introduction. The purpose of this project is to build a coded Hex Calculator that does the following operations:. - Multiply. - Square of a number.
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Coded Hex Calculator With signed & Unsigned Caluclations Project Done By: Apurva Patel Vrajesh Patel Swapna Kalakonda
Introduction • The purpose of this project is to build a coded Hex Calculator that does the following operations: - Multiply -Square of a number - Addions of signed and Unsigned Numbers - Subtractions of signed and Unsigned Numbers - Division - Signed Division
Multiplication case 1: - Multiplying two negative numbers--> will give the answer in positve so we will take the abs of the two numbers and then multiply: the abs function (Absolute Value Function): -This function will take the 2s’ complement of the number if the number is negative (signed) case 2: If a positive number is multiplied by a negative number then for sure the ans is going to be negative. For the ans to be negative we will take the abs of that negative number and then do a normal multiply and to show that the ans is negative will turn on the LED showing the negative sign. case 3: when both are positive then we will do the regular multiply
Sigmul.Whp : SM* (A B -- +(A*B)) OVER OVER /2Dup A B A B XOR 80 AND /n = ((A xor B) and 80h) --To check wheather only /one of them is negative DUP /A B n n >R /A B n ?ABS /call to the routine ?ABS to take the absolute /values of negative numbers either A or B or /both * /call to the normal unsigned multiplication routine /for multiplying / C = |A|*|B| R> /C n IF /if n = 1 the answer is negative indicated by /pushing 80h into 80 LD! / LED register THEN ;
Square This routine multiplies the input number by itself. The following is the whyp file for square. : SQUARE (A -- A*A ) DUP / A A * ; /call to unsigned multiplication routine for multiplying A*A
Unsigned Division How to do Unsigned Division to get 16-bit Quotient and a 8-bit remainder. * In order to get a 16-bit quotient we need to carry out the normal division two times. * Each time we will get a 8-bit quotient. * This routine will not give us an overflow unless a number is divided by 00h.
unsigndiv.whp : MU/MOD (NL NH D -- R Q)/THIS ROUTINE DIVIDES /16-BIT NUMERATOR WITH /8-BIT DENOMINATOR TO /GIVE 8-BIT QIUOTIENT AND /8-BIT REMAINDER -ROT /D NL NH DIV DIV DIV DIV DIV DIV DIV DIV ROT_DROP_SWAP ; /R Q : UM/MOD (NL NH D -- R QL QH) >R 00 R@ /NL NH 00 D D MU/MOD /R QHD R> /R QH D SWAP /R D QH >R /R D QH MU/MOD /R2 QL QH R> ; /R2 QL QH
Signed Division This takes in a 16-bit signed numerator and an 8-bit Denominator Therefore, the sign numbers can be broken down into the following categories: 1. 0000h to 7FFFh --> Positive numbers 2. 8000h to FFFFh --> Negative numbers The following are the cases for signed division: Divident Divisor Quotient Remainder Negative Negative Positive Negative Negative Positive Negative Negative Positive Negative Negative Positive Positive Positive Positive Positive
Signdiv.whp : DIVIDE* (NL NH D -- R QL QH) OVER OVER AND /NL NH D NH D 80 AND IF /NH<0 D<0 --> QLQH>0 AND R<0 ABS -ROT DABS /|D| |NL| |NH| ROT UM/MOD /R QL QH WAITBTN3 /R QL QH DROP DROP 0= /R IF /IF R = 0 NO NEED TO SHOW NEGATIVE SIGN 00 LD! /ELSE LIGHT UP THE SIG LED ELSE 80 LD! /SHOWS REMAINDER IS NEGATIVE THEN ELSE /EITHER NUMERATOR OR DENOMINTOR < 0 OR BOTH > 0 0< IF /D<0 AND NLNH >0 --> QLQH<0 AND R>0 ABS /NL NH |D| UM/MOD /R QL QH 0= >R SWAP 0= /CHECKS WHEATHER QUOTIENT IS ZERO OR NOT >R SWAP R> R> AND
Cont... IF /IF QUOTIENT IS ZERO NO NEED TO SHOW THE /NEGATIVE SIGN 00 LD! ELSE 80 LD! THEN WAITBTN3 00 LD! /R QL QH DROP DROP /R ELSE -ROT /D NL NH 0< /CHECKS WHEATHER NUMERATOR < 0 IF /D>0 AND NLNH<0 --> R<0 AND QLQH<0 DABS /D |NLNH| ROT UM/MOD /R QL QH 0= >R SWAP 0= /CHECKS WHEATHER QUOTIENT IS ZERO OR NOT >R SWAP R> R> AND
Cont... IF /IF QUOTIENT IS ZERO NO NEED TO SHOW THE /NEGATIVE SIGN 00 LD! ELSE 80 LD! THEN WAITBTN3 /R QL QH DROP DROP /R 0= IF /CHECKS WHEATHER QUOTIENT IS ZERO OR NOT 00 LD! ELSE 80 LD! THEN ELSE /D>0 NLNH>0 --> R>0 QLQH>0 ROT /NL NH D UM/MOD /R QL QH WAITBTN3 /R QL QH DROP DROP /R THEN THEN THEN ;
Signed Subtraction Case 1: Subtracting when both the numbers are negative: subcase 1: if B>A then get a positive answer else get a negative answer Case 2: When one of A or B is a negative number subcase 1: if A ‘+ve’ and B ‘-ve’ then ans = A + B else if A ‘-ve’ and B is ‘+ve’ then ans = -(A+B) Case 3: when both are positive ans = A-B and the ans is postive or neg depending on the magnitude of A and B
Signsub.whp : S- (A B -- A-B) 0< /checks wheather B<0 IF /B<0 SWAP /B A 0< /checks wheather A<0 IF /A<0 and B<0 - 0< / C = B-A IF /checks wheather C<0 ABS ELSE 80 LD! THEN ELSE /B<0 and A>0 SWAP ABS + /C = A-(-B) 0< /if C<0 It is a overflow IF FF LD! /Indicates a overflow THEN THEN ELSE SWAP 0< IF /B>0 and A<0 ABS + /C = -A-B 0< /If C is negative indicates a overflow /else answer is negative and 2'scomplement /of C
Cont... IF FF LD! ELSE 80 LD! THEN ELSE /A>0 and B>0 SWAP - /C = A - B 0< IF /if B>A then answer is negative and 2'scomplement of ABS /of C 80 LD! THEN THEN THEN ;
Changes Made to The W8Y controller Changed from Mux2g to mux 3g Input from 16x8 Dpram N2 ALU4 Output Y2 of ALU4
Whyp Words Added to W8Y controller * mpp : Carries out the multiplication of the numbers in the data stack when called 8 times * divide: carries out the division of the numbers in the data stack when called 8 times to leave a 8-bit quotient and 8-bit remainder * ABS: takes the absoloute value of the number in T-Reg * DABS: Takes the 2s complement of a 16-bit number and leaves the higher 8-bit in T-Reg and the lower 8-bits in N-Reg
User’s Guide 1. First enter the code for the operation to be carried out. Project 1 operations: hex code operation 01h signed subtraction 02h unsigned multiplication 03h Square 04h signed multiplication Project 2 operations: hex code operations 01h unsigned division 02h signed division If the entered hex code is different from the above codes all the LEDs will Light up indicating a NULL operation. 2. Enter the required hex values
Cont … user guide * For division enter the lower 8-bits of numerator first and followed by higher 8-bits followed by the denominator * Press BTN3 to enter the values through the switches. * Negative numbers will be indicated by turning on the most significant LED by pushing 80h in the LD-reg * Overflow is indicated by lighting up all the LEDs
