Computer Arithmetic in Practice

Appendices

Appendix A. Range of numbers

Numerical range for BIN, 2's and SM formats for assumed n and m, where n is the number of bits of the integer part (quotient), m is the number of bits of the fractional part.

Table A.1 Range for n + m = 8 Bits

n	m	Resolution 2−m	Range for decimal format
			BIN	2's	SM
8	0	1.0	0:255	−128:127	−127:127
7	1	0.5	0:127.5	−64:63.5	−63.5:63.5
6	2	0.25	0:63.75	−32:31.75	−31.75:31.75
5	3	0.125	0:31.875	−16:15.875	−15.875:15.875
4	4	0.0625	0:15.9375	−8:7.9375	−7.9375:7.9375
3	5	0.03125	0:7.96875	−4:3.96875	−3.96875:3.96875
2	6	0.015625	0:3.984375	−2:1.984375	−1.984375: 1.984375
1	7	0.0078125	0:1.9921875	−1:0.9921875	−0.9921875: 0.9921875
0	8	0.00390625	0:0.99609375	−0.5:0.49609375	−0.49609375:0.49609375 ...