Binary
Unit 4 Summary - Part 2
Inside a computer there are millions of on/off electrical switches.
On is 1 (one) while Off is 0 (zero).
These on-off switches make electronic numbers, they are called Binary.
The more the binary number goes to the left, the amount is doubled.
CONVERSIONS
Convert Binary to Decimal
(Decimal is also called Denary or Base 10)
Convert Decimal to Binary
Binary Addition
Rules:
0 + 0 = 0
0 + 1 = 1
1 + 1 = 0 carry 1
1 + 1 + 1 = 1 carry 1
Binary Substraction
Binary Left & Right Shifts
Binary Multiplication
Binary Division
Convert a minus decimal to binary using
two's complement
Oxford AQA IGCSE 2019
01.2.
State the decimal representation of the binary number 10101010. [1 mark]
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Answer:
Put the binary in this table:
Start calculating every top row that has 1 in it: 128+32+8+2 = 170
01.3.
What is the largest decimal number that can be represented using 8 bits? [1 mark]
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The answer is 255, remember this.
Put all 1 in all columns, you'll get this calculation:
128+64+32+16+8+4+2+1 = 255.
14.1.
A binary shift of two places left is to be applied to the binary number 00101011
Write the result of applying the binary shift in the table below. [1 mark]
Answer:
The binary is actually 101011. Drag it 2 columns to the left. So now it becomes 10101100.
14.2.
What is the arithmetic effect of a binary shift left by two places?
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Answer:
The number is multiplied by 4 (because each column is twice bigger than the column on their right).
Oxford AQA IGCSE 2020
01.2.
State the decimal representation of the binary number 01000010 [1 mark]
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01.3.
State what binary shift would have to be applied to the binary number 00111000 to double it. [1 mark]
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01.4.
Add the following two binary numbers together. [1 mark]
0 1 0 1 0 0 0 0
+ 0 0 0 1 0 0 1 0
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Oxford AQA IGCSE Specimen Paper
01.1.
Convert the decimal number 107 to binary. [1 mark]
Final Answer:
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01.3.
State two reasons why programmers often use hexadecimal instead of binary. [2 marks]
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01.4.
What is the largest decimal number that can be represented using 6 bits? [1 mark]
Final Answer:
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01.5.
Using binary arithmetic, add together the binary numbers 00111001 and 01010010, giving your answer in binary.
Show your working. [2 marks]
Final Answer:
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Oxford AQA IGCSE Mock Paper
01.
Figure 1 shows the contents of a byte of memory in binary.
Figure 1
01.1.
State the contents of the byte in Figure 1 in decimal. [1 mark]
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13.1.
Using binary arithmetic, add together the binary numbers 00010100 and 00110101, giving your answer in binary.
Show your working. [2 marks]
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13.2.
The binary number 00101100 has been produced by applying a shift to the binary number 00001011.
Explain what shift has been applied. [2 marks]
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