A 4-bit unsigned integer holds the value 1110 (14). You add 0011 (3). What does the hardware store as the result?
A0001 (1), because the carry-out is discarded when the result exceeds 4 bits
B1111 (15), which is the maximum 4-bit value
C0000 (0), because overflow sets the register to zero
D10001 (17), stored by automatically expanding to 5 bits
14 + 3 = 17 = 10001 in binary. Only the lower 4 bits (0001 = 1) are stored; the carry-out is simply discarded. The hardware does not raise an error or expand storage — detecting overflow is the programmer's responsibility via the carry flag.
Question 2 Multiple Choice
When computing 0111 + 0001 in 4-bit binary, how many carry operations are generated?
A0 — there are no carries because both numbers are small
B1 — only the rightmost column produces a carry
C3 — carries ripple through three consecutive columns
D4 — every column carries
Rightmost: 1+1=10, write 0, carry 1. Second: 1+0+carry=10, write 0, carry 1. Third: 1+0+carry=10, write 0, carry 1. Leftmost: 0+0+carry=1, no carry. Result: 1000 (8). Carries ripple through three columns — this chain is called carry propagation and directly determines how fast hardware adders operate.
Question 3 True / False
When a binary addition overflows a 4-bit register, the processor automatically raises a hardware error and halts execution.
TTrue
FFalse
Answer: False
Overflow does not halt execution. The hardware discards the carry-out bit and stores only the lower bits of the result. The processor may set a carry or overflow flag in a status register, but the programmer must explicitly check it. Undetected overflow is a real source of bugs in systems programming.
Question 4 True / False
In binary addition, a carry is generated whenever the sum of bits in a column — including any incoming carry — equals or exceeds 2.
TTrue
FFalse
Answer: True
This is the binary analog of carrying in decimal, where you carry when a column sum reaches 10. Since binary digits max at 1, any column total of 2 or more generates a carry of 1 into the next more-significant position.
Question 5 Short Answer
Why do hardware designers prefer to implement subtraction as addition with a negated operand, rather than building a separate subtraction circuit?
Think about your answer, then reveal below.
Model answer: Because a single adder circuit can handle both operations. In two's complement, negation is cheap — just flip all bits and add 1. This means the same adder handles subtraction at almost no extra hardware cost, keeping circuit complexity low.
Building two separate circuits would roughly double arithmetic hardware complexity. Two's complement makes negation so inexpensive that the subtraction path is just: negate the second operand, then add. This is why two's complement representation was adopted universally — the hardware savings are significant.