Solve the following.
(a)Multiply : 11111110000011 to 101.
(b) Add : 10101010101011 with 1001.
Answers
Step-by-step explanation:
Unit 1 Section 3 : Multiplying Binary Numbers
Long multiplication can be carried out with binary numbers and is explored in this section.
Note that multiplying by numbers like 10, 100 and 1000 is very similar to working with base 10 numbers.
Example 1
Calculate the binary numbers:
(a) 1011 × 100
(b) 110110 × 1000
(c) 11011 × 10000
Example 2
Calculate the binary numbers:
(a) 1011 × 11
(b) 1110 × 101
(c) 11011 × 111
(d) 11011 × 1001
Exercises
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Question 1
Calculate the binary numbers:
(a) 111 × 10
(b) 1100 × 100
(c) 101 × 1000
(d) 11101 × 1000
(e) 10100 ÷ 10
(f) 1100 ÷ 100
Check your answers by converting to base 10 numbers.
Question 2
Calculate the binary numbers:
(a) 111 × 11
(b) 1101 × 11
(c) 1101 × 101
(d) 1111 × 110
(e) 11011 × 1011
(f) 11010 × 1011
(g) 10101 × 101
(h) 10101 × 111
(i) 10101 × 110
(j) 100111 × 1101
Question 3
Solve the following equations, where all numbers, including x, are binary:
(a)
x = 110
11
x =
(b)
x = 101
101
x =
(c)
x = 111
10
x =
(d)
x = 1011
111
x =
Question 4
Multiply each of the following binary numbers by itself:
(a) 11
(b) 111
(c) 1111
What do you notice about your answers to parts (a), (b) and (c)?
What will you get if you multiply 11111 by itself?
Answer:
00000000000000000000 a
000000⁰0000000000000 b