OCR J277 - Binary Arithmetic Revision Tool

1 [2 Marks]

Add the following two 8-bit binary numbers.

0 0 1 1 0 1 0 0
+ 0 0 0 1 1 0 1 1
_______________

💡0+1=1, 1+1=10, 1+1+1=11

✅ Mark Scheme

Answer: 0100 1111

(Working: Carries should be shown correctly for full marks if written exam, here self-assess method).

Score yourself (Max 2):

2 [3 Marks Total]

Add the following two 8-bit binary numbers.

1 1 1 1 0 0 0 1
+ 0 0 0 0 1 1 1 1
_______________

(a) Write the 8-bit binary result. [2] (b) State the name of the error that has occurred. [1]

✅ Mark Scheme

(a) 0000 0000 (100000000 is 9 bits, so 8-bit result is all zeros).

(b) Overflow (error).

⚠️ Common Mistake Do not write "Stack Overflow" or "Out of Memory". Just "Overflow".

Score yourself (Max 3):

3 [3 Marks Total]

(a) Perform a Binary Shift Left of 2 places on: 0000 1110. [1]

(b) Explain the mathematical effect of a Left Shift of 1 place. [1]

(c) Describe the binary shift required to divide any binary number by 4. [1]

✅ Mark Scheme

(a) 0011 1000

(b) Multiplies the number by 2.

(c) Right shift of 2 places.

Score yourself (Max 3):

4 [3 Marks Total]

A student performs a Right Shift of 1 place on 0001 0101 (21).

(a) Write the result of this shift. [1] (b) The correct answer to 21 ÷ 2 is 10.5. Explain why your binary shift result is not exactly 10.5. [2]

✅ Mark Scheme

(a) 0000 1010

(b) Explanation:

Binary shifts work with integers only (1).
The fractional part (0.5) is lost / loss of precision (1).

Score yourself (Max 3):

5 [2 Marks]

Perform a binary shift to multiply 0000 0101 by 8.
Show the resulting 8-bit binary number.

💡Hint: x2 = 1 shift. x4 = 2 shifts. x8 = ?

✅ Mark Scheme

Answer: 0010 1000

(Obtained by Left Shift of 3 places)

Score yourself (Max 2):

6 [3 Marks]

Explain what happens to the Most Significant Bit (MSB) during a Left Shift of 1 place if the MSB is already a 1.

✅ Mark Scheme

The bit falls off the end of the register / is lost (1).
This causes an overflow error / result becomes invalid (1).

Score yourself (Max 3):