Give step-by-step solution with explanation and final answer:
Generate a flowchart for the algorithm below, then write an assembly function that implements it and meets the criteria.
- The function a

Question

Give step-by-step solution with explanation and final answer: 
Generate a flowchart for the algorithm below, then write an assembly function that implements it and meets the criteria.
- The function accepts two parameters:
-The array of 16-bit integers is passed by reference on the stack, i.e. the address of the first element is passed.
- The length of the array in elements (not bytes) is passed by value as a 16-bit integer in register D.
- The function returns a 16-bit integer in D, which is the 16-bit Internet checksum of the array.
- The function must preserve registers (other than D).
- The function must not use specific memory storage for any local variables, i.e. all local variables must be stored on the stack.
- The function may assume that the length is non - zero.

VIPSolutions · Accepted Answer

Let's break down the solution step by step: --- ## 1. **Flowchart for the 16-bit Internet Checksum Algorithm** The **Internet checksum** sums up all 16-bit words in the data, adds carries back into the sum, and then returns the one's complement of the result. ### **Internet Checksum Algorithm Steps** 1. **Initialize sum = 0** 2. **For each word in the array:** - sum += word 3. **If sum > 0xFFFF**, add carry to the lower 16 bits - while (sum > 0xFFFF): sum = (sum & 0xFFFF) + (sum >> 16) 4. **One's complement of sum** 5. **Return sum** --- ### **Flowchart** ``` +---------------------+ | Start | +---------------------+ | v +---------------------+ | sum = 0 | +---------------------+ | v +---------------------+ | i = 0 | +---------------------+ | v +-------------------------------+ | i < length? | +-------------------------------+ | Yes v +-------------------------------+ | sum = sum + array[i] | +-------------------------------+ | v +-------------------------------+ | i = i + 1 | +-------------------------------+ | v +---------------------+ | [Back to check i < length] | | v No | v +-------------------------------+ | while (sum > 0xFFFF): | | sum = (sum & 0xFFFF) + | | (sum >> 16) | +-------------------------------+ | v +-------------------------------+ | sum = ~sum (one's complement) | +-------------------------------+ | v +---------------------+ | Return sum | +---------------------+ ``` --- ## 2. **Assembly Function** Assume: - **Stack**: First parameter (array address) is at 2(SP) (after return address). - **D**: Contains length (16-bit). - **Return value**: D. - **Preserve all registers except D**. - **Local variables** must be on the stack (no .BSS or .DATA). - **Assembly syntax**: I'll use a generic 68K/M68000 style assembly (common in embedded courses). Adjust for your platform as needed. --- ### **Step-by-step Implementation** #### **Stack Usage** - Save registers (A0, A1, etc. if used). - Local variables on stack: - sum (32 bits, because sum can overflow 16 bits). - i (16 bits). #### **Algorithm** 1. sum = 0 2. i = 0 3. Loop: - If i >= length: break - sum += array[i] - i++ 4. Fold carry: while (sum > 0xFFFF): sum = (sum & 0xFFFF) + (sum >> 16) 5. sum = ~sum 6. Return sum (in D) --- ### **Assembly Pseudocode (68K style)** ```assembly ; Function: internet_checksum ; Params: ; - 2(SP): address of array (by reference) ; - D: length (number of elements) ; Returns: D = checksum ; Clobbers: D only ; Preserves: All other registers ; Local vars: sum (32-bit), i (16-bit) on stack internet_checksum: LINK A6,#-8 ; Allocate 8 bytes local stack frame (sum: 4 bytes, i: 2 bytes, align) MOVEM.L D1-D2/A0,-(SP) ; Save used registers CLR.L -(A7) ; sum (32 bits) at [A6 - 4] (offset -4) CLR.W -(A7) ; i (16 bits) at [A6 - 6] (offset -6) MOVE.W D0,D1 ; D1 = length (save length) MOVE.L 8(A6),A0 ; A0 = array address (from stack) CLR.W -6(A6) ; i = 0 loop: MOVE.W -6(A6),D2 ; D2 = i CMP.W D2,D1 ; i < length ? BGE done ; if not, exit loop MOVE.W (A0,D2.W*2),D2 ; D2 = array[i] (each element is 2 bytes) EXT.L D2 ; Sign extend to 32 bits MOVE.L -4(A6),D0 ; D0 = sum ADD.L D2,D0 ; D0 += array[i] MOVE.L D0,-4(A6) ; sum = D0 ADDQ.W #1,-6(A6) ; i++ BRA loop done: ; Fold carry: while (sum > 0xFFFF): sum = (sum & 0xFFFF) + (sum >> 16) MOVE.L -4(A6),D0 ; D0 = sum fold_carry: MOVE.L D0,D2 AND.L #$FFFF0000,D2 BEQ fold_done MOVE.W D0,D1 ; D1 = lower 16 bits SWAP D0 ; D0 = upper 16 bits in lower word CLR.W D0 ; D0 = upper 16 bits (in lower word) ADD.W D1,D0 ; D0 = lower 16 + upper 16 MOVE.W D0,D0 ; Zero upper word MOVE.L D0,D0 ; D0 = sum (lower 16 bits + carry) BRA fold_carry fold_done: NOT.W D0 ; One's complement ANDI.W #$FFFF,D0 ; Ensure 16 bit MOVEM.L (SP)+,D1-D2/A0 ; Restore registers UNLK A6 RTS ``` --- ### **Explanation** - **sum** is stored as a 32-bit value on the stack to accommodate overflow. - **i** is a 16-bit loop counter, also on the stack. - All temporary values and registers except D are preserved. - Only the stack is used for local variables. - The checksum is returned in D (as required). --- ## **Fi

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