The Wey Valley School & Sports College
Mathematics Home Study
Page 1
BINARY NUMBERS ↔ BASE 10
1.
Convert each of the following binary numbers to base 10
a) 11
b) 1011
c) 11101
d) 100011
e) 101101
f) 1001001
g) 110010
h) 111101
i) 110111
2.
Write each of the following base 10 numbers as binary
numbers:
a) 12
b) 38
c) 15
d) 61
e) 102
f) 90
g) 82
h) 44
i) 56
3.
a) What is the largest possible binary number with 5 digits?
b) What is the smallest possible binary number with 5 digits
c) Convert your answers to (a) and (b) to base 10.
UNIT: Binary Numbers
Support work:
Page 1
Core work:
Page 2
Extension work: Page 3
REMEMBER: 1011001 = 64 + 16 + 8 + 1 = 89
27
128
26
64
1
25
32
0
24
16
1
23
8
1
22
4
0
21
2
0
20
1
1
The final digit should always be in the 20 column.
Challenge – For this challenge do not use a calculator and you
must be able to justify how you arrived at your answer:
What is the largest power of 2 that divides 127 – 1?
2
A 21
B 27
C 28
D 263
Page 2
BINARY CALCULATIONS
1) Calculate the following, in binary arithmetic:
a) 1+1
b) 1 + 10
c) 11 + 101
d) 111 + 101
e) 110 + 101
f) 111 + 111
g) 11011 + 1101
h) 1110 + 1011
i) 11011 + 11101
2) Calculate the following, in binary arithmetic:
a) 11 – 1
b) 10 – 1
c) 111 – 100
d) 1011 – 110
e) 1111 – 101
f) 1000 – 11
g) 10000 – 1110
h) 11010 – 1101
i) 110111 – 1101
3) Calculate the following, in binary arithmetic:
a) 1101 x 10
b) 10110 x 100
c) 11101 x 1000
d) 1010100 ÷ 100
E 2127
Page 3
BINARY MULTIPLICATION, EQUATIONS &
OTHER BASES
1) Carry out these multiplications, in binary arithmetic:
a) 101 x 11
b) 111 x 1101
c) 1011 x 110
d) 10001 x 111
e) 10011 x 110
2) Multiply each of the following binary numbers by itself:
a) 1
b) 10
c) 1101
d) 1011
e) 10011
3) Solve these equations, where all the numbers are binary
numbers:
a)
x – 111 = 1010
b)
x – 101 = 1101
c)
x + 11 = 110
d)
x + 111 = 1101
e)
x – 1011 = 1101
f) x + 10111 = 11100
4) Convert the following from the base stated to base 10:
a)
122 base 3
b) 314 base 4
c)
142 base 5
d) 1125 base 6
e)
178 base 9