converting between denary & binary

what is denary?

denary is a number system that is made up of 10 digits (0-9), also known as the base-10 number system.

true or false?

humans use the binary system for counting and performing math calculations.

false.

humans use the denary system for counting, measuring, and performing math calculations.

define binary.

binary is a number system that is made up of two digits (1 and 0), also known as the base-2 number system.

why do computers use binary?

computers use binary numbers to represent data because they are built using transistors that can only be in a state of on or off, which fits the binary number systems of 1s and 0s.

true or false?

at GCSE level, you will be asked to convert from/to binary up to and including 16 binary digits.

false.

at GCSE level, you will only be asked to convert from/to binary up to and including 8 binary digits (8 bits).

what is the denary range you will work with when converting to/from binary at GCSE level?

at GCSE level, you will work with a denary range of 0-255 (00000000-11111111 in binary).

convert the following binary number to denary.

128	64	32	16	8	4	2	1
1	0	1	0	1	1	0	0

128 + 0 + 32 + 0 + 8 + 4 + 0 + 0 = 172

convert the following binary number to denary.

128	64	32	16	8	4	2	1
0	1	1	1	0	0	0	1

0 + 64 + 32 + 16 + 0 + 0 + 0 + 1 = 113

convert the following binary number to denary.

128	64	32	16	8	4	2	1
1	0	0	1	0	0	0	0

128 + 0 + 0 + 16 + 0 + 0 + 0 + 0 = 144

convert 76 to binary.

128	64	32	16	8	4	2	1
0	1	0	0	1	1	0	0

convert 150 to binary.

128	64	32	16	8	4	2	1
1	0	0	1	0	1	1	0

convert 94 to binary.

128	64	32	16	8	4	2	1
0	1	0	1	1	1	1	0