Numbers in base two numerals

Multiplication of Two Digit Binary Numbers

When multiplying binary numbers, it is important to note that:

0 × 0 = 0

1 × 0 = 0

0 × 1 = 0

1 × 1 = 1

Examples:

Multiply the following leaving your answers in binary:

(i) 11₂ × 11₂  (ii) 101₂ × 11₂  (iii) 1011₂ × 101₂

Solutions:

(i) 11₂ × 11₂ = 112×11211+1110012

(ii) 101₂ × 11₂ = 1012×112101+10111112

(iii) 1011₂  × 101₂ = 10112×101210110000+10111101112

Note: Teacher should explain with more examples very well in class.

CLASS ACTIVITY

1. Multiply the followings:
2. 11o11₂ x 1111₂ 10000111₂  x  111001₂
3. Find the product of 23 and 11₂ in base two (Hint: Covert 23 to a binary number)

Quantitative Aptitude Reasoning on Number Bases

Sample A:

ASSIGNMENT

1. Calculate 110₂ × (1011₂ + 1001₂ – 101₂)
2. Find the value of the following, leaving your answers in base two: (a) The square of 110₂  (b) (1000₂)²

PRACTICE QUESTIONS

1. Calculate the product of these binary numbers.

(a) 111 × 10

(b) 1100 × 100

(c) 101 × 1000

(d) 111 × 11

(e) 1101 × 101

(f) 1101 × 11

(g) 1111 × 110

2. (a) Multiply the base 10 numbers 15 and 13

(b) Convert your answers to a binary number.

(c) Convert 15 and 13 to binary numbers.

(d) Multiply their binary conversion.

(e) Compare your answer in (b) to (d)