The positions (from left to right) correspond to powers of two: (2^{15}) down to (2^0). Only bits at positions (2^{14}) and (2^1) are set to 1 (since the string has a 1 in the second position and another 1 in the second-to-last position). Thus:
0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
So, as a pure binary number, 0100000000010000 equals the decimal integer . 2. A Glimpse into Computer Architecture This number, 16386, is not random either. It sits precisely one above 16385, which is (2^{14} + 1). But more interestingly, consider if this 16-bit string were not data, but an instruction in a simple processor’s instruction set architecture (ISA). In many early 16-bit CPUs (like the PDP-11 or the 6502 with 16-bit addressing), the first few bits of an instruction denote the opcode, and the rest specify registers or memory addresses.
The positions (from left to right) correspond to powers of two: (2^{15}) down to (2^0). Only bits at positions (2^{14}) and (2^1) are set to 1 (since the string has a 1 in the second position and another 1 in the second-to-last position). Thus:
0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
So, as a pure binary number, 0100000000010000 equals the decimal integer . 2. A Glimpse into Computer Architecture This number, 16386, is not random either. It sits precisely one above 16385, which is (2^{14} + 1). But more interestingly, consider if this 16-bit string were not data, but an instruction in a simple processor’s instruction set architecture (ISA). In many early 16-bit CPUs (like the PDP-11 or the 6502 with 16-bit addressing), the first few bits of an instruction denote the opcode, and the rest specify registers or memory addresses. 0100000000010000