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Consider Figure $\text{A}$ and Figure $\text{B}$ which represent $4$ bit signed and unsigned numbers respectively in $2’s$ complement system.

Assume that a few variables are defined below and initialized in such a way that places them in the spot shown in Figure $\text{C}$.

int s1, s2, s3; unsigned int u1, u2, u3;

Which of the following(s) is/are true?

- $s3 > u3$
- $s1 > s3$
- $u1 > u3$
- $s1 > u3$

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We can take integers as $k$ bits in the system. For an easy explanation, we are taking $k =4$.

Let

$s1 = 1001

s3 = 0010$

$u1 = 1010

u3 = 0001$

$s3$ and $u3$ will be $2$ and $1$ in decimal, respectively, irrespective we treat them as signed numbers or unsigned numbers (MSb is $0$).

$s1$ is $9$ in unsigned and $-7$ in signed.

$u1$ is $10$ in unsigned and $-6$ in signed.

Option $\text{A}$:

This is an unsigned comparison i.e., $s3$ will be treated as an unsigned number.

Although MSB of $s3$ is $0$ hence, it does not matter.

$s3 > u3$ is same as $2 > 1$, which is true

Option $\text{B}$:

both are signed hence signed comparison

$s1 > s3$ is same as $-7 > 2$, which is false.

Option $\text{C}$:

both are unsigned hence unsigned comparison

$u1 > u3$ is same as $10 > 1$, which is true.

Option $\text{D}$:

one of the variables is unsigned hence unsigned comparison

$s1 > u3$ is same as $9 > 1$, which is true.

Let

$s1 = 1001

s3 = 0010$

$u1 = 1010

u3 = 0001$

$s3$ and $u3$ will be $2$ and $1$ in decimal, respectively, irrespective we treat them as signed numbers or unsigned numbers (MSb is $0$).

$s1$ is $9$ in unsigned and $-7$ in signed.

$u1$ is $10$ in unsigned and $-6$ in signed.

Option $\text{A}$:

This is an unsigned comparison i.e., $s3$ will be treated as an unsigned number.

Although MSB of $s3$ is $0$ hence, it does not matter.

$s3 > u3$ is same as $2 > 1$, which is true

Option $\text{B}$:

both are signed hence signed comparison

$s1 > s3$ is same as $-7 > 2$, which is false.

Option $\text{C}$:

both are unsigned hence unsigned comparison

$u1 > u3$ is same as $10 > 1$, which is true.

Option $\text{D}$:

one of the variables is unsigned hence unsigned comparison

$s1 > u3$ is same as $9 > 1$, which is true.