OCR J277 Mark Scheme - Binary Arithmetic

OCR	GCSE (9-1) Computer Science Mark Scheme J277/01: Unit 1.2 Binary Arithmetic & Shifts

Question	Answer	Marks	Guidance
1	Working: Carries shown correctly (e.g., carrying the 1s above/below the line) (1) Answer: 0100 1111 (1)	2	AO2 (Application) Examiner Note: J277 requires students to show working to gain full marks if specified. If the answer is correct but no working is shown, award 1 mark only (depending on strictness of the year's mark scheme, but usually working is credited separately). If answer is wrong but working shows correct carry method, award 1 mark.
2a	Working: Carries shown correctly (specifically the carry out of the byte) (1) Answer: 0000 0000 (1)	2	AO2 (Application) The sum is 100000000 (9 bits). The question asks for the 8-bit result, which is just the eight zeros. Accept (1) 0000 0000 or 1 0000 0000 as long as the student understands the 8-bit limitation.
2b	Overflow (error)	1	AO1 (Knowledge) Must use the term "Overflow". Do not accept "Out of memory" or "Stack overflow".
3a	0011 1000	1	AO2 (Application) Check that 2 zeros have been added at the right and the bits moved left.
3b	It multiplies the number by 2	1	AO1 (Knowledge) Both "Multiply" and "2" are required.
3c	Right shift of 2 places	1	AO1 (Knowledge) Right shift 1 = ÷ 2, Right shift 2 = ÷ 4.
4a	0000 1010	1	AO2 (Application) The original right-most '1' falls off the end.
4b	A binary shift works with integers (whole numbers) only (1). So the fractional part (0.5) is lost / loss of precision occurred (1).	2	AO2 (Application) Key concept: Loss of precision. Accept "The bit fell off the end of the register".
5	0010 1000 (2) (1 mark for Left Shift of 3 places implied)	2	AO2 (Application) x 8 requires a shift of 3 places. Original: 0000 0101 (5) -> Shift 3: 0010 1000 (40) Award 1 mark if they shifted left but by wrong amount (e.g. 2 or 4 places).
6	The bit is lost / falls off the end of the register (1). This causes an overflow error / the number becomes incorrect (significantly smaller) (1).	2	AO1 (Knowledge) Students need to recognise that shifting a '1' out of the MSB destroys the value of the number, similar to the addition overflow.