GCSE A451 - Binary and Hex

Question 1

Calculate the denary value of the 8-bit binary number 10010111. Explain working out. (2)

Answer 1

• 128 + 16 + 4 + 2 + 1

- 151

Question 2

Add the following two 8-bit binary numbers and explain the result.

1 0 0 1 0 1 1 1
+
1 1 0 1 1 0 0 0

Answer 2

1 0 0 1 0 1 1 1
1 1 0 1 1 0 0 0
0 1 1 0 1 1 1 1
1 (extra bit/overflow) 1



• There is an overflow
• The answer cannot be represented in 8-bits

Question 3

Convert hexadecimal number 6A to denary. Explain your working out (2)

Answer 3

• 6 * 16 (= 96) / 10 (for A)

- 106

Question 4

Convert hexadecimal number 6A to binary. Explain your working out (2)

Answer 4

0110 1010

Question 5

Convert binary number 0 01 1 1 1 0 1 to hexadecimal. Explain your working out (2)

Answer 5

3D

Question 6

Explain why hexadecimal numbers are often used to represent binary numbers (2)

Answer 6

Hex numbers are shorter
… and can easily be converted to and from binary…
… as each hex digit corresponds to 4 binary digits

Question 7

Convert the denary value 55 into an 8-bit binary number. Explain working out. (2)

Answer 7

0011 0111

Question 8

Convert the denary value 55 into hexadecimal (2)

Answer 8

37

Question 9

Explain why computers use binary (2)

Answer 9

So that computers can be based on logic circuits.
… ( each part of the circuit) can be in one of two states
… 0 and 1/true or false

Question 10

Explain how instructions are stored in binary (2)

Answer 10

-The instruction consists of an op code (instruction)

… and an operand (address of data)