Number Representations & States

"how numbers are stored and used in computers"

E4M3

Try editing the 8 bit floating point value below.

0
sign
0000
exponent
000
mantissa
=(023)×2(1 - 7)=0×2-7=0

  E4M3Each row is the first four bits, and each column is the second four bits.

 
0000...
0001...
0010...
0011...
0100...
0101...
0110...
0111...
1000...
1001...
1010...
1011...
1100...
1101...
1110...
1111...
...0000
+0
0.03125
0.125
0.5
2
8
32
128
-0
-0.03125
-0.125
-0.5
-2
-8
-32
-128
...0001
0.001953
0.035156
0.140625
0.5625
2.25
9
36
144
-0.001953
-0.035156
-0.140625
-0.5625
-2.25
-9
-36
-144
...0010
0.003906
0.039063
0.15625
0.625
2.5
10
40
160
-0.003906
-0.039063
-0.15625
-0.625
-2.5
-10
-40
-160
...0011
0.005859
0.042969
0.171875
0.6875
2.75
11
44
176
-0.005859
-0.042969
-0.171875
-0.6875
-2.75
-11
-44
-176
...0100
0.007813
0.046875
0.1875
0.75
3
12
48
192
-0.007813
-0.046875
-0.1875
-0.75
-3
-12
-48
-192
...0101
0.009766
0.050781
0.203125
0.8125
3.25
13
52
208
-0.009766
-0.050781
-0.203125
-0.8125
-3.25
-13
-52
-208
...0110
0.011719
0.054688
0.21875
0.875
3.5
14
56
224
-0.011719
-0.054688
-0.21875
-0.875
-3.5
-14
-56
-224
...0111
0.013672
0.058594
0.234375
0.9375
3.75
15
60
240
-0.013672
-0.058594
-0.234375
-0.9375
-3.75
-15
-60
-240
...1000
0.015625
0.0625
0.25
1
4
16
64
256
-0.015625
-0.0625
-0.25
-1
-4
-16
-64
-256
...1001
0.017578
0.070313
0.28125
1.125
4.5
18
72
288
-0.017578
-0.070313
-0.28125
-1.125
-4.5
-18
-72
-288
...1010
0.019531
0.078125
0.3125
1.25
5
20
80
320
-0.019531
-0.078125
-0.3125
-1.25
-5
-20
-80
-320
...1011
0.021484
0.085938
0.34375
1.375
5.5
22
88
352
-0.021484
-0.085938
-0.34375
-1.375
-5.5
-22
-88
-352
...1100
0.023438
0.09375
0.375
1.5
6
24
96
384
-0.023438
-0.09375
-0.375
-1.5
-6
-24
-96
-384
...1101
0.025391
0.101563
0.40625
1.625
6.5
26
104
416
-0.025391
-0.101563
-0.40625
-1.625
-6.5
-26
-104
-416
...1110
0.027344
0.109375
0.4375
1.75
7
28
112
448
-0.027344
-0.109375
-0.4375
-1.75
-7
-28
-112
-448
...1111
0.029297
0.117188
0.46875
1.875
7.5
30
120
+NaN
-0.029297
-0.117188
-0.46875
-1.875
-7.5
-30
-120
-NaN