AQA AS Computing Representing Data 2
Fixed Point Binary
In denary we represent number, or parts of numbers, that are less than one like this:
100 10 1 . 1/10 1/100 1/1000
3 6 9 . 7 5 2
In binary, we use the same tactic:
1 1
8 4 2 1 . ½ ¼ /8 /16
1 0 1 0 . 1 1 0 0
10 . 75 (10)
Converting fixed point binary to denary
Convert the integer part as normal, then add the fractions together:
0.1(2) = ½ = 0.5(10)
0.01(2) = ¼ = 0.25(10)
1
0.001(2) = /8 = 0.125(10)
1
0.0001(2) = /16 = 0.0625(10)
Converting denary to fixed point binary
Convert the integer part as normal, then remove the fractions:
E.G. 11.6875 [ = 1010.1011]
Integer part = 1010(2)
Remove 0.5 from the fractional part = 1010.1(2) Remaining: 0.1875(10)
Can’t remove 0.25 from the fractional part = 1010.10(2) Remaining: 0.1875(10)
Remove 0.125 from the fractional part = 1010.101(2) Remaining: 0.0625(10)
Remove 0.0625 from the fractional part = 1010.1011(2) Remaining: 0(10)
AQA AS Computing Representing Data 2
Binary Multiplication
Binary multiplication uses the following rules (obvious when you think about it):
0x0=0
0x1=0
1x0=0
1x1=1
E.G. 1 – 1100 x 0010 [ = 11000]
1100
0010 x
Multiply by the right hand number: 0000
Multiply by the next number: 1100
Multiply by the next number: 0000
Multiply by the next number: 0000 0
11000
We can effectively ignore any 0s in the bottom number.
E.G 2 – 0010 1010 x 0001 0010 [ = 1 1010 0100]
00101010
00010010 x
00101010
00101010 0+
110100100
