CUET PG 2022 — Computer PYQ
CUET PG | Computer | 2022The product of two four bit positive binary numbers 1011 and 0011 is _________
Choose the correct answer:
- A.
1000011
- B.
100001
(Correct Answer) - C.
100101
- D.
100111
100001
Explanation
The product of two four bit positive binary numbers 1011 and 0011 is
100001. Step 1: Convert binary numbers to decimal
The first binary number is
. Its decimal equivalent is calculated as:
The second binary number is
. Its decimal equivalent is calculated as:
101121011 sub 2
10112
1×23+0×22+1×21+1×20=11101 cross 2 cubed plus 0 cross 2 squared plus 1 cross 2 to the first power plus 1 cross 2 to the 0 power equals 11 sub 10
1×23+0×22+1×21+1×20=1110
001120011 sub 2
00112
0×23+0×22+1×21+1×20=3100 cross 2 cubed plus 0 cross 2 squared plus 1 cross 2 to the first power plus 1 cross 2 to the 0 power equals 3 sub 10
0×23+0×22+1×21+1×20=310Step 2: Calculate the product in decimal
Multiply the two decimal values:
11×3=331011 cross 3 equals 33 sub 10
11×3=3310Step 3: Convert the product back to binary
Convert the decimal product
to binary using repeated division by 2. Reading the remainders from bottom to top yields the binary result:
.
331033 sub 10
3310
1000012100001 sub 2
1000012