Signed-Magnitude Binary Division

Signed-magnitude binary division is a method of dividing binary numbers in which the sign bit is considered separately from the magnitude bits. The sign bit indicates whether the number is positive or negative, while the magnitude bits represent the absolute value of the number.

Division of (11100)2 by (10011)2

To divide (11100)2 by (10011)2 using signed-magnitude binary division, we follow these steps:

Step 1: Determine the sign of the quotient

Since both the dividend and divisor are positive, the sign of the quotient will also be positive.

Step 2: Align the most significant bit of the divisor with the most significant bit of the dividend

We add leading zeros to the divisor so that it has the same number of bits as the dividend. This ensures that the most significant bit of the divisor is aligned with the most significant bit of the dividend.

(11100)2 dividend
(10011)2 divisor

(11100)2 dividend
(10011)2 divisor
(00100)2 divisor (after adding leading zeros)

Step 3: Subtract the divisor from the dividend

We start by subtracting the divisor (10011)2 from the leftmost four bits of the dividend (1110)2. The result is (1011)2, which becomes the leftmost four bits of the quotient.

(11100)2 dividend
(10011)2 divisor
(00100)2 divisor (after adding leading zeros)

1011 quotient
-1001 (divisor)
-----
0100 remainder

Step 4: Bring down the next bit of the dividend

We bring down the next bit of the dividend (0) and append it to the remainder (0100)2. This gives us (01000)2, which we use as the new dividend.

(11100)2 dividend
(10011)2 divisor
(00100)2 divisor (after adding leading zeros)

1011 quotient
-1001 (divisor)
-----
0100 remainder

01000 new dividend

Step 5: Divide the new dividend by the divisor

We start by subtracting the divisor (10011)2 from the leftmost three bits of the new dividend (100), but we get a negative result. This means that we need to add the divisor back to the remainder and bring down the next bit of the dividend.

(11100)2 dividend
(10011)2 divisor
(00100)2 divisor (after adding leading zeros)

1011 quotient
-1001 (divisor)
-----
0100 remainder

01000 new dividend

00100 (divisor)
- 01000 (new dividend)
-----
11100 remainder (after adding back the divisor)

Step 6: Bring down the next bit of the dividend

We bring down the next bit of the dividend (0) and append it to the remainder (11100)2. This gives us (111000)2, which we use as the new dividend.

(11100)2 dividend
(10011)2 divisor
(00100)2 divisor (after adding leading zeros)

1011 quotient
-1001 (divisor)
-----
0100 remainder

01000 new dividend

00100 (divisor