What is a half adder
A half adder is a circuit that takes two inputs, A and B, and produces two outputs, S (the sum of A and B) and C out (the carry out)
What does a 1‑bit half‑adder compute?
It computes the Sum and Carry of adding two single bits A and B.
What is the Boolean expression for the Sum output of a half‑adder?
Sum = A XOR B.
What is the Boolean expression for the Carry output of a half‑adder?
Carry = A AND B.
What additional input does a full adder have compared to a half adder?
A full adder has a carry‑in (Cin) input.
What does a full adder compute?
It computes the Sum and Carry‑out (Cout) of adding A, B, and Cin.
What is the Boolean expression for the Sum output of a full adder (canonical form)?
Sum = A’B’C + A’BC’ + ABC + AB’C’.
What is the simplified Boolean expression for the Sum output of a full adder using XOR?
Sum = A ⊕ B ⊕ C.
What is the simplified Boolean expression for the Carry output of a full adder?
Carry = A.B + C. (A ⊕ B)
Why is the carry output of a full adder 1?
Because at least two of the inputs (A, B, Cin) are 1.
How do you build an n‑bit adder from full adders?
Connect full adders in series so that each adder’s carry‑out becomes the next adder’s carry‑in.
What is the main limitation of a ripple‑carry adder?
The carry must propagate through all stages, causing delay.
What range of integers can be represented using 4‑bit 2’s complement?
From −8 to +7.
How do you detect overflow in 2’s complement addition (without guard bit)?
Occurs when adding two numbers with the same sign produces a result with the opposite sign.
If the first number when using 2’s complement is a 1/0 what does it mean
1 = negative number
0 = positive number
How does the guard bit detect overflow?
Overflow occurs when the guard bit of the result differs from the MSB (most significant bit) of the n‑bit result.
When does arithmetic overflow happen
When the guard bit in the result is different from the most significant bit of the 4-bit representation
How is subtraction implemented using an adder?
A − B is computed as A + (2’s complement of B).
How do you form the 2’s complement of B in hardware?
Invert all bits of B (1’s complement) and add 1 via setting the initial carry‑in to 1.
How does a single circuit perform both addition and subtraction?
Use a mode bit (switch mode/ SM):
SM = 0 → addition
SM = 1 → subtraction (invert B and set Cin = 1)
How can multiplication be performed using repeated addition?
Multiply A × B by adding A to itself B times.
What is binary long multiplication?
A method where each bit of the multiplier selects a shifted version of the multiplicand, and the partial products are added.
What happens when we multiply by powers of 2
Its a case of shifting a bit pattern to the left e.g.
14 x 2 = 1110 x 10 = 11100
14 x 4 = 1110 x 100 = 111000
Multiplying by 2^n = shift left by n positions
What are the three main types of shift operations?
Logical shifts, arithmetic shifts, and circular (rotate) shifts.
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History of Computer Science32
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Von Neumann and Harvard Architecture45
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Parallelism, Memory and Amdahl's Law36
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Data Representation45
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Data Storage23
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Representing Real Data19
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Real Numbers Instructions54
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Instruction Execution - week 719
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Operand Modes - Week 713
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Control Instructions - Week 738
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Pipelining and Superscalar Architectures - Week 817
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Input/Output - Week 834
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Handling Input/Output - Week 944
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Boolean Logic and Circuits - Week 916
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Boolean Logic and Circuits - Week 1011
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Application of Karnaugh Maps - Week 102
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Implementing Arithmetic - Week 1028
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Sequential Logic - Week 1128
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Flip Flops - Week 1127
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Intro to Operating Systems34
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OS lecture 8 - Design36
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OS Lecture 9 - Threads and Processes (1)48
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OS lecture 10 - Threads and Processes (2)54
